Complex interaction of polarized light with three-dimensional opal-based photonic crystals: Diffraction and transmission studies

Polarization characteristics of light interaction with the photonic crystal of a-SiO₂ synthetic opals were studied under the conditions of low dielectric contrast. We analyzed 3D diffraction patterns of monochromatic light and calculated optical transmission spectra of oriented samples. The diffraction patterns are found to change with the polarization of incident light, indicating a strong polarization dependence of photonic stop bands in synthetic opals. It is shown theoretically there exists a critical angle, θ_c, of the p-polarized light incident on the (h k l) crystal plane, at which the resonance contribution to Bragg diffraction vanishes.     

Design of photonic bands for opal-based photonic crystals

To make a device from an opal—or otherwise—the photonic bands and the optical properties derived from them are needed. Knowing the effects of different parameters defining the opal geometry and different possible modifications of its structure are needed, too. An accurate definition of the device will be required to obtain a good performance. With this aim, the optics of light with a wavevector in the vicinity of the L point in the Brillouin zone and its coupling to bare opals band structure are presented. An important aspect is the transition from finite to infinite crystal and the study of size effects on the bands. It is possible to substantially alter the photonic band structure of an opal-based system, while maintaining the lattice structure, simply by growing layers of other materials with an appropriate refractive index. Here, it is shown how, by the growth of accurately controlled thin layers of silicon and germanium, and further processing, one can induce the opening of two complete photonic band gaps (PBGs) in an opal structure. Finally, the possibility to fabricate a simple device consisting in a planar waveguide will be shown. By means of a very simple and inexpensive procedure, engineered planar defects acting as microcavities have been realized. These can be viewed as a particular case of a much more general class of heterostructures that can be grown by combining opal vertical deposition and chemical vapour deposition of oxides. A further step is made by applying electron beam lithography to provide lateral definition and facilitate three-dimensional structuring.     

Template assisted fabrication technique towards Si-inverse opals with diamond structure

A method to fabricate silicon (Si) inverse opals with diamond structure is introduced. The method is based on the arrangement of silica particles in a template consisting of Si pillars periodically distributed. The profile of the pillars is specially designed to induce the self-organized growth of the particles in a diamond lattice along the (1 1 0) direction. Afterwards, the inverse structure is achieved by infiltrating the opal with Si and subsequently removing the silica by chemical means. Different from a former approach based on robotic manipulation, this method allows the fabrication of large samples available for integration in planar photonic devices.     

Modification of photonic properties in porphyrin-infiltrated opal crystals

Structural, optical and magnetic properties of porphyrin-infiltrated opal hybrid structures were investigated. Bulk samples of synthetic opal were grown by sedimentation technique from colloidal solution of SiO₂ spheres of diameter 250 nm. The structure of the samples was examined by atomic force microscopy. The photonic properties of crystals were investigated by optical measurements in transmission and reflection modes. The stop band was observed in the region 510–550 nm. The photonic properties of synthetic opal crystals were modified by infiltration with aqueous basic solution of iron–porphyrin (FeTPPS) of concentration 1.0 mM. In hybrid samples the absorption bands typical of FeTPPS were observed in the vicinity of the opal stop band. Magnetic properties of FeTPPS-infiltrated opal samples have been studied at 5–300 K in magnetic fields up to 5 T. The FeTPPS-infiltrated opal crystals can be considered as the structures perspective for magnetophotonic devices.     

Polarization insensitive self-collimation waveguide in square lattice annular photonic crystals

The frequency bands for self-collimation at both TE and TM polarizations in square lattice annular photonic crystals are studied systematically by plane-wave expansion and finite difference time domain methods. By increasing the inner ring radius or reducing the outer ring radius, the self-collimation band will be moved to a lower frequency. Compared with the TM modes, TE ones have different frequency sensitivities to both the inner ring radius and outer ring radius tuning. Using these features, a polarization insensitive self-collimation waveguide in a high dielectric contrast system with bandwidth up to 102.9 nm is demonstrated as an example of the implementation of photonic integration circuits.     

Highly birefringent photonic crystal fiber polarization splitter made of soft glass

A soft glass dual core polarization splitter based on highly birefringent photonic crystal fiber (PCF) is proposed and the full vector finite element method (FEM) is employed to analyze the impacts of structural parameters on birefringence and the coupling length, and simulation results show that high birefringence on the order of 10⁻² can be obtained at 1.55 μm, moreover, hole size, hole pitch and elliptic ratio all affect birefringence and the coupling length. Based on these results, the PCF's structure is optimized to realize a polarization splitter of 282 μm whose largest extinction ratio is around −45.42 dB at 1.55 μm. Meanwhile, the bandwidth at the extinction ratio of −10 dB is about 90 nm, and around 32 nm at −20 dB.     

Localized photonic modes in photonic crystal heterostructures

In this work, interface modes of two-dimensional photonic crystal heterostructures have been investigated by usage of the supercell method. The photonic crystal heterostructure is made of two photonic crystals with square symmetry in which one of them is composed of circular dielectric rods in air background and the other one is constructed by drilled square holes in dielectric. It is shown that using of a proper supercell plays an important role in obtaining the correct interface modes. We have also showed that the guided interface modes and single mode which is different from those reported in some published works are nearly dispersionless.     

Multiple slow light bands in photonic crystal coupled resonator optical waveguides constructed with a portion of photonic quasicrystals

Coupled resonator optical waveguides (CROWs) in complex two-dimensional (2D) photonic crystals (PCs) constructed with a portion of 12-fold photonic quasicrystals (PQs) are proposed. We show that enhanced transmission and slow light can be simultaneously achieved in such waveguides as well as general CROWs. Moreover, due to higher degree of flexibility and tunability of PQs for defect mode properties compared to conventional periodic PCs, multiple slow light bands can be flexibly obtained in CROWs constructed with complex 2D PCs. Our results may lead to the development of a variety of novel ultracompact devices for photonic integrated circuits.     

Properties of defect modes in one-dimensional symmetric defective photonic crystals

We theoretically investigate the properties of defect modes in one-dimensional symmetric defective photonic crystals. We consider three defective photonic crystal structures, air/[(AB)^NsA^α(BA)^Ns]^Np/air, air/[(AB)^NsAB^βA(BA)^Ns]^Np/air, and air/{[(AB)^NsAB^βA(BA)^Ns]B^γ}^Np−1[(AB)^NsAB^βA(BA)^Ns]/air, where A and B are respectively taken to be the high- and low-index dielectric materials. The first has a defect layer of A^α, the second has a composite defect, AB^βA, and the third has a interleaving defect B^γ. The effect of thickness on the defect mode is studied by varying the parameters α, β, and γ, respectively, for the above model structures. It is found that the positions and the number of defect modes can be significantly changed due to the change in the defect thickness. In addition, by increasing the repeated number N_p, we can have multiple defect modes, leading to a possible design of tunable multichannel filter.     

Superprism properties in 2D polymer photonic crystals at high normal frequencies

The superprism effects of higher bands, i.e., for normal frequencies of higher than one, in two-dimensional (2D) polymer photonic crystals (PCs) are investigated. It is shown that in a polymer PC of triangular symmetry with filling factor of about 31%, the gradual transition of the hexagonal into triangular equi-frequency dispersion contours leads to a strong superprism in the 6th band at a normal frequency of 1.2. This dispersion is more prominent than those observed in the lower bands in 2D PCs. Also, this requires a lattice constant longer than the concerned wavelength. Furthermore, in a 2D polymer PC with a filling factor of about 83% a strong discontinuous superprism effect occurs at normal frequencies higher than one, which is due to an abrupt transition between two modes with the refraction angles of opposite signs. The effect can be exploited for switching applications as demonstrated in the paper.     

Novel optical modulator using silicon photonic crystals

We propose a novel compact and integrated optical modulator, which consists of p–i–n silicon photonic crystals with triangular lattice and a line defect waveguide. The device operation is based on a dynamic shift of the photonic band gap (PBG), which induced change in the silicon refractive index by the free carrier injection. We have numerically analyzed and investigated its light modulation performance by using plane wave expansion (PWE) method and finite-difference time-domain method. With small size, rapid response time and high extinct ratio, the designed optical modulator can be used in photonic integrated circuits.     

Modelling of 3D photonic crystals based on opals

The construction of 3D photonic crystals with gaps in the visible or the near-infrared frequency range requires engineering of complex microstructures which are very difficult to realize by etching and micro-fabrication. Consequently, self-ordered systems such as synthetic opals are very promising. Synthetic bare opals are constituted by SiO₂ spheres that organize themselves by a sedimentation process in a face centered cubic (fcc) arrangement. Using the plane wave method, we examine the photonic band structures of close-packed opal-based photonic crystals with an SiO₂ (n = 1.5) matrix. The incomplete photonic band gaps at the X- and L-points have been studied which correspond to normally incident plane waves onto the (100) and (111) crystal planes. With the transfer matrix method, we model the transmission properties. We find that the incomplete gap at the L-point fully inhibits the transmission of waves propagating in the [111] direction for opal sample thicknesses that are easily obtainable. This property shows that bare opals could be good candidates for complete inhibition of transmission in the near-infrared and visible frequency range for given orientations.     

Spectroscopy of the photonic stop band in synthetic opals

The photonic band gap of opals has been studied experimentally from their optical transmission spectra as a function of the incident beam orientation in the opal crystal lattice. The measurements were carried out for all high-symmetry points on the surface of the Brillouin zone of an fcc lattice. The experimental dependence of the energy position of the photonic band gap on the light wave vector direction is well described by the set of theoretical relations developed for the stop bands originating from the Bragg diffraction of light on {111}-type planes of the twinned fcc lattice of synthetic opals.     

Band gap studies of 2D photonic crystals with hybrid scatterers

Two-dimensional (2D) photonic crystals (PCs) of a square lattice with dielectric hybrid rods in air are proposed; these PCs consist of a square rod at the center of the unit cell and additional circular rods with their outermost edges against the middle of each side of the lattice unit cell. The band gap structures of PCs can be tailored and optimized by rotating the square rods and adding circular rods to the lattice unit cell. The variation of bands near the complete photonic band gap boundaries, due to some specific modes, is sensitive to certain structural parameters of the system. The results can be understood by analyzing the spatial energy distribution of the electromagnetic fields. Based on such a field analysis, a novel interpretative model is proposed. The PC can be fabricated easily and operated in the microwave region and, hence, should be suitable for applications in new microwave devices.     

Enhanced complete photonic band gap in the optimized planar diamond structure

The diamond photonic crystal with dielectric rods has been modified to enlarge the fundamental band gap. By planarizing the diamond structure and reducing the thickness of the hexagonal meshes, the band gap can be increased substantially. The band gap is 29% for a refractive index contrast of 3.6. The modified structure is amenable to fabrication at optical and infrared wavelengths using state-of-the-art silicon-processing methods. Transfer matrix calculations demonstrate a large attenuation within the band gap.     

Antireflection film in one-dimensional metallo-dielectric photonic crystals

We calculated the transmittance of a one-dimensional (1D) metallo-dielectric photonic crystal (MDPC) in the optical region including the absorption losses in metal layers. The structure consists of five Ag and four GaN layers stacked alternately. When we add an antireflection coating to each end of the stack, the transmittance of the MDPC is increased twice as much and the oscillations in the transmission spectrum are also smoothed out compared with the case without them. The transmittance for oblique incident angles is also increased by the addition of two antireflection layers at the ends of the 1D MDPC.     

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals

A detailed derivation of eigenvalue equation in two dimensional and three dimensional photonic crystals is given by the plane-wave expansion method. Some mathematical formulas such as the rotation of vector, the gradient of scalar, the divergence of the vector, the vector triple product and the conversion between scalar and vector are employed. The eigenvalue equation in photonic crystals has become the important base for obtaining the band structure and the distribution of eigenmode.     

Microcavity filters based on hexagonal lattice 2-D photonic crystal structures embedded in ridge waveguides

Two-dimensionally periodic photonic crystal microcavity filters in a ridge waveguide format have been designed and fabricated. Transition mode-matching features were added to increase the optical throughput by more than a factor of two. An increase of Q-factor (more than 100%) was achieved by the addition of two further rows of photonic crystal holes to the microcavity filters. Attempts have also been made to tailor the filter response by applying design concepts used in other Bragg-grating optical filter technologies.     

General representation of interference contrast formed by arbitrarily polarized waves and its application in wave design for holographic fabrication of photonic crystals

A general formula of interference contrast formed by two arbitrarily polarized elliptical waves propagating along arbitrary directions in three-dimensional (3-D) space is derived. From it a series of inferences for the interference of linear and circular waves including their different combinations are obtained. These formulae are used for polarization optimization in three and four noncoplanar beam interference for the fabrication of 3-D periodic microstructures. The numerical calculations show that the use of circular light can improve the uniform contrast considerably compared with the use of only linear light, and the use of elliptical light may make the contrast even higher.     

All optical switch based on Fano resonance in metal nanocomposite photonic crystals

We investigate the potential of plasmonic resonance in metal nanocomposite materials for the design of photonic crystal all optical switches by numerical methods. We study the absorption effect of the plasmonic resonance on the Fano resonances of one dimensional photonic crystal slabs covered by a metal nanocomposite layer. It is shown that the absorption reduces the contrast of the Fano resonances. However, for adequate metal nanoparticle concentrations it is possible to achieve both sufficiently sharp Fano resonance and strong Kerr nonlinearity, which provides a suitable condition for the design of high contrast and low threshold switches.