Analysis of the imperfection of opal-like photonic crystals synthesized on conducting substrates

The type and degree of imperfection for opal-like photonic crystals on conducting substrates have been investigated using synchrotron small-angle X-ray scattering with a microradian resolution. It has been demonstrated that self-assembly of poly(styrene) spheres by the vertical deposition method leads to the formation of a face-centered cubic structure on a mica/Au substrate and a random hexagonal close packing on a glass substrate with the In₂O₃(SnO₂) conducting coating.     

Electromagnetic modes in semi-infinite photonic crystals

In a real photonic crystal, there exist three modes: propagation mode, evanescence mode and surface mode. Using ideal modal, semi-infinite photonic crystals, we study their effects on the transmission spectrum of photonic crystals, respectively. Because there exists only one air–crystal interface in a semi-infinite photonic crystal, no multiple reflection occurs and no evanescent modes and backward-propagating modes exist in this structure. The effects of the evanescence modes are studied by comparing the transmission spectrum of a finite-thickness photonic crystal slab and that of a semi-infinite photonic crystal. In addition, the effects of the backward-propagating modes are investigated using a coated semi-infinite photonic crystal structure. Finally, we study the effects of the surface modes, and find that the transmission spectrum of a semi-infinite photonic crystal is strongly dependent on its termination.     

Band-edge-induced Bragg diffraction in two-dimensional photonic crystals

Two-dimensional photonic crystals composed of two orthogonal volume diffraction gratings have been photogenerated in photopolymers. When the read beam is set at the Bragg angle, the diffraction efficiency of the transmission grating is strongly enhanced at the band edge of the reflection grating recorded in the material. Such a device provides Bragg operation and enhancement of the diffraction efficiency of the thin diffraction grating together with good wavelength selectivity. Such advantages could be interesting for optical signal processing.     

Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.     

Enhanced second-harmonic generation for multiple wavelengths by defect modes in one-dimensional photonic crystals

We present an effective design of aperiodically stacked layers of nonlinear material and air, sandwiched by two truncated photonic crystals, in terms of the simulation annealing method. The constructed structure can achieve multiple-wavelength second-harmonic generation (SHG) at the preassigned wavelengths. We derive a general solution of SHG in 1D inhomogeneous systems and apply it to evaluate the SHG conversion efficiency. Numerical simulations show that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequencies are assigned to the designed defect states.     

Properties of single and multiple defect modes in one-dimensional photonic crystals containing left-handed metamaterials

Wave propagation is studied in structures consisting of alternate left- and right-handed layers.Bragg gap and zero-n gap appear in different frequency regions of the structure.The periodicity of the structure is broken by simply reversing the order of the layers in one half of the structure,resulting in defect modes located inside the zero-n gap and Bragg gap.These modes can be made very narrow by adding more layers in the structure.The defect mode located inside the zero-n gap is sensitive to the symmetry of the structure and insensitive to the angle of incidence of the incoming radiation.Multiple modes are also generated inside the gaps by repeating the structural pattern.Thus,a simple structure can be used for single and multiple modes that are important for different applications.     

Bloch waves and non-propagating modes in photonic crystals

We investigate the propagation of electromagnetic waves in finite photonic band gap structures. We analyse the phenomenon of conduction and forbidden bands and we show that two regimes are to be distinguished with respect to the existence of a strong field near the interfaces. We precise the domain for which an effective medium theory is sounded.     

Optical spectra of one-dimensional defect photonic crystals

The effect exerted by defects that represent a local disturbance of the structural periodicity on the band spectrum of a one-dimensional photonic crystal has been investigated. A classification of single defects has been proposed. It has been demonstrated that the position of defect minibands in the band gap of the spectrum of the crystal can be controlled by varying the type of a defect and its location in the crystal structure. The presence of two defects in the structure leads to the formation of two minibands, so that the spacing between the minibands and their intensity depend on the type of defects and on the distance between them.     

Transition of lasing modes in disordered active photonic crystals

The transition from a photonic band-edge laser to a random laser in two-dimensional active photonic crystals is described. The lasing modes in the active photonic crystals shift from the edge of the photonic bandgap to the bulk of the gap when a certain amount of position and size disorder is introduced. The shift of lasing modes is determined with various gain profiles. The results show that the modulation of lasing modes is significant when the lasing transition wavelength overlaps the photonic bandgap.     

Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals

Magnetic photonic crystals are periodic arrays of lossless materials, at least one of which being magnetically polarized. Magnetization, either spontaneous or induced, is associated with nonreciprocal effects, such as Faraday rotation. Magnetic photonic crystals of certain configuration can also display strong spectral asymmetry, implying that light propagates in one direction much faster or slower than in the opposite direction. This essentially nonreciprocal phenomenon can result in electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic waves of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction. The frozen mode has zero group velocity and drastically enhanced amplitude. The focus of our investigation is the frozen mode regime. Particular attention is given to the case of weak nonreciprocity, related to the infrared and optical frequencies. It appears that even if the nonreciprocal effects become vanishingly small, there is still a viable alternative to the frozen mode regime that can be very attractive for a variety of practical applications.     

Tamm states and nonlinear surface modes in photonic crystals

We predict the existence of surface gap modes, known as Tamm states for electronic systems, in truncated photonic crystals formed by two types of dielectric rods. We investigate the energy threshold, dispersion, and modal symmetries of the surface modes, and also demonstrate the existence and tunability of nonlinear Tamm states in binary photonic crystals with nonlinear response.     

Tunneling modes in photonic crystals with anisotropic single-negative metamaterials

We study tunneling modes in a one-dimensional photonic crystal (1DPC) with multilayered periodic structures containing dispersive anisotropic single-negative (ASNG; permittivity- or permeability-negative) metamaterials. A defect layer is introduced into the proposed structure, and some unusual properties are found in contrast with that of a tunneling mode in PCs with isotropic single-negative (SNG) gaps.     

Localized defect modes in finite magnetic two-dimensional photonic crystals

We present a detailed study of localized defect modes in finite two-dimensional magnetic photonic crystal consisting of cylindrical ferrite material in air background by using the scattering matrix method. It is shown that due to having positive and negative value of the effective magnetic permeability in interested photonic band gap, the defect modes present different behavior. Our results show that the modes appeared in positive permeability region have features similar to the modes supported by the dielectric photonic crystal while those created in the negative permeability region are strongly localized at the interface of defect ferrite rod with air background. Moreover, results indicate that defect modes occurred in the negative region are sharper than those appeared in the positive one which means the quality factor of former case is extremely high.     

Structure of light scattering spectra in opal photonic crystals

Spectra of light losses are studied at a fixed angle of incidence of a collimated beam on the surface of an opal anisotropic photon crystal at various observation angles. It is shown that the structure of the forward-and backscattered light spectra is connected with the existence of several directional photonic forbidden bands. It is demonstrated that back scattering is enhanced and forward scattering is suppressed in the frequency region of photonic forbidden bands. It is suggested that a scattering band associated with photon localization at the photonic gap edge is observed.     

Optical surface modes of photonic crystals for dual-polarization waveguide

In this study, the design of a polarization-independent (dual-polarization) waveguide is presented by utilizing surface modes of photonic crystals. The waveguide structure operates in a frequency interval that is commonly shared by both transverse-electric (TE) and transverse-magnetic (TM) polarizations. The numerical calculations based on plane wave expansion and finite-difference time-domain methods are carried out to design and demonstrate a surface mode waveguide that provides confinement and guiding for both TE and TM modes. Once the relevant modes are properly excited, the high transmission efficiency of the photonic crystal surface waveguide is ensured. The demand to have polarization-insensitive devices makes our proposed design an important component for the photonic integrated circuit applications. Finally, we also propose a broadband surface mode photonic crystal waveguide with a bandwidth value of 28% for only TE polarization.     

Self-trapping and stable localized modes in nonlinear photonic crystals.

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.     

Direction-selective optical transmission of 3D fcc photonic crystals in the microwave regime

Three-dimensional (3D) photonic crystal exhibit direction-selective transmission with respect to the center frequency of the stop gap. As a model system, the stop gap of a 3D fcc inverted-opal photonic crystal is studied in the microwave regime in detail using 3D polyamide models. The difference in the direction-selective transmittance between crystals grown in two different high symmetry directions is experimentally shown and compared to numerical simulations.     

Acoustooptic interaction in two-dimensional photonic crystals: Efficiency of Bragg diffraction

We obtain equations for the Bragg regime of acoustooptic diffraction of light in two-dimensional photonic crystals. We determine applicability conditions of the single-wave approximation, in which it is sufficient to take into account only one Fourier component of each of Bloch waves involved in the acoustooptic interaction. In the single-wave approximation, we obtain formulas that make it possible to estimate the acoustooptic figures of merit of a photonic crystal. We show that, in a photonic crystal, higher acoustooptic figures of merit can be achieved than in the materials that make up the crystal.     

Two types of additional absorption spectra in CaF2 crystals

A study of two types of additional absorption spectra observed in colored CaF₂ crystals is reported. The spectral shape for the additively colored crystal is governed by the experimental conditions; during photochemical coloring, it depends on the thermal prehistory of the sample. In all cases, a spectrum consisting of bands at 370 and 560 nm appears in crystals having a band near 200 nm. An additional band appears at 560 nm in the Smakula spectrum at high-irradiation doses; there are three stages in the increase of this band with increasing dose. A similar dependence on the radiation dose is observed for the 560-nm band in synthesized CaF₂ crystals. It is suggested that this band is due to defects produced in the lattice during the irradiation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 56–64, April, 1969.     

Defect modes of chiral photonic crystals with an isotropic defect

Specific features of the defect modes of cholesteric liquid crystals (CLCs) with an isotropic defect, as well as their photonic density of states, Q factor, and emission, have been investigated. The effect of the thicknesses of the defect layer and the system as a whole, the position of the defect layer, and the dielectric boundaries on the features of the defect modes have been analyzed. It is shown that when the CLC layer is thin the density of states and emission intensity are maximum for the defect mode, whereas when the CLC layer is thick, these peaks are observed at the edges of the photonic band gap. Similarly, when the gain is low, the density of states and emission intensity are maximum for the defect mode, whereas at high gains these peaks are also observed at the edges of the photonic band gap. The possibilities of low-threshold lasing and obtaining high-Q microcavities have been investigated.