Tunable multichannel filter in photonic crystal heterostructure containing permeability-negative materials

A tunable multichannel filter is demonstrated theoretically based on a one-dimensional photonic crystal heterostructure containing permeability-negative material. The filtering properties of the photonic crystal filter, including the channel number and frequency, can be tuned by adjusting the structure parameters or by a pump laser. The angular response of the photonic crystal filter and the influences of the losses on the filtering properties are also analyzed.     

Multichannel filtering properties of photonic crystals consisting of single-negative materials

The multichannel filtering properties have been investigated by means of the transfer-matrix method in the one-dimensional periodic structures containing two kinds of single-negative materials. Two sets of comb-like filtering channels appear simultaneously on the two sides of the bandgap with zero-effective phase. One is omnidirectional in the low frequency, and the other is angle-sensitive in the high frequency. The multichannel filtering properties of the structures, such as the channel number, the central frequencies and quality factors, may be modified by adjusting the period number and the layer thicknesses. It thus provides a simple way to design multichannel filter with specific channels.     

Complete evanescent tunneling gaps in one-dimensional photonic crystals

Complete band gaps are found in one-dimensional photonic crystals composed of negative-permittivity and negative-permeability materials. The mechanism of these complete band gaps, unlike the Bragg complete gaps formed by interferences of forward/backward propagating waves, originate from the evanescent wave tunneling in the single-negative materials is reported for the first time. Moreover, it is also reported for the first time that both Bragg complete gaps and evanescent wave tunneling complete gaps exist in a three-constituent one-dimensional photonic structure simultaneously.     

Negative refraction in a honeycomb-lattice photonic crystal

In this paper we theoretically investigate a photonic crystal with dielectric rods in a honeycomb lattice. Two left-handed frequency regions are found in the second and third photonic band by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Subwavelength imaging by the photonic crystal flat lens are systematically studied by numerical simulations using the multiple scattering method. Different from the photonic crystals with noncircular dielectric rods in air, this structure is almost isotropic at the optimal frequency for superlensing. As a comparison, flat slab focusing is also demonstrated at other frequencies in the two left-handed regions.     

Large forbidden angles for a two-dimensional photonic crystal of connected-honeycomb lattice

The off-plane band structures of a two-dimensional photonic crystals of connected-honeycomb lattice are calculated by the plane-wave expansion method. To investigate how the band gaps vary with the off-plane angle, an effective refractive-index model is employed to work out the corresponding angular gap map. We find that the connected-honeycomb lattice can provide forbidden angles taking up as much as 58.6% of the solid angle. The result will be helpful in the design of photonics devices incorporating two-dimensional photonic crystal structures.     

Experimental study of quasi-one-dimensional comb-like photonic crystals containing left-handed material

Quasi-one-dimensional comb-like photonic crystals with backbone waveguide made of left-handed material are physically fabricated by using transmission lines. The transmission properties are experimentally investigated and it is found that the structures possess a special band gap. The gap does not originate from the conventional Bragg scattering mechanism in that it is invariant with the change of scale length. Moreover, the experimental results indicate that the gap-edges are determined by zero-average permittivity of the branch and backbone and zero permeability of backbone, respectively. Because of the characteristics, it will be convenient to realize a special gap using in microwave and optical engineering.     

Focusing Properties in Photonic Crystal Structure Formed by Air Holes in Dielectric Background with Concave Interface

We investigate the focusing properties of photonic crystal structures with a concavo-concave as the photonic crystal boundary. The photonic crystal is constituted by air holes parallelly distributed in a uniform dielectric. A good-quality focus of a plane wave can appear out of the photonic crystal structure, and a strong far field focus is also formed from the photonic crystal interface. A negative-refractive beam at the frequency 0.195 （2πc/α） for the excited Bloch wave mode near the Brillouin zone edges under all incident angles are obtained by simulation.     

Optical Tamm States in Dielectric Photonic Crystal Heterostructure

We investigate one-dimensional dielectric photonic crystal and optical Tamm modes formed by superposition of two band gaps and find that this kind of mode can be explained by the single negative materials tunnelling effect. A finite-size dielectric photonic band gap can mimic one kind of effective single negative material and this property sensitively depends on the frequency location in stop-band regions and surface termination and so on. The effective impedance match and effective phase match give the precise position of the optical Tamm mode. Complete transparency via tunnelling is achieved by two opaque media and demonstrates the validity of our approach.     

Characteristics of guided waves in indefinite-medium waveguides

We have presented a discussion on the guided waves in the indefinite-medium waveguides. The characteristic equations describing TE and TM guided waves have been derived. Aiming mainly at the TE guided waves, we have analyzed the existence conditions for the guided and surface modes for four distinct cases, respectively. A number of exotic properties have been revealed in such waveguides, such as the coexistence of forward and backward modes, the absence of fundamental modes, the existence of surface modes and the relaxed requirements for waveguide core constitutive parameters. Numerical results have confirmed our analyses.     

Study on maximum band gap of two-dimensional photonic crystal with elliptical holes

In this paper, the maximum photonic band gap (PBG) of two-dimensional (2D) photonic crystal (PC) with elliptical air holes was studied by the finite-difference time-domain (FDTD) method based on changing the ratio (semi-major axis length of elliptical hole to the filling ratio) and azimuth angle of elliptical holes, respectively. It is shown that the PBG exhibits a peak value when the ratio of semi-major axis length to the filling ratio is equal to 0.86 approximately by increasing the filling ratio, and central frequency and the low boundary frequency of PBG decrease linearly with the increasing of semi-major axis length. In the aspect of the influence of azimuth angle from 0 to 90°, the PBG presents a minimum value, and central frequency and the low boundary frequency of PBG become high non-linearly by the increasing of azimuth angle to any filling ratio.     

Study on complete band gap of two-dimensional photonic crystal with quadrangular rods

The plane wave expansion method (PWM) was employed to study the relation between the photonic band gap (PBG) of 2D triangular lattice photonic crystal (PC) and the shapes of rods and dielectric constant. It is shown that the PBG of PC with quadrangular rods is the widest one, compared with the other case with cross section shapes of triangular, circular and hexagon under the same filling ratio, and a peak value appears when the side length ratio of l_x/l_y is equal to 1.21 approximately to any filling ratio. In the aspect of the effects of dielectric constant, the PBG width does not increase monotonically with the increase permittivity ?₂ of the background material to certain permittivity ?₁ of the quadrangular rods, but has a peak value instead. However, the larger the permittivity ?₁ is, the narrower the band width is and the lower the central frequency is, and the dispersion Δ? = ?₂ − ?₁ is larger also.     

Beaming effect in multimode photonic crystal by using coupled waveguides

Beaming effect of a multimode photonic crystal (PC) covered by a waveguide array on the exit plane is investigated theoretically. The simulation results show that the multimode PC can make the incident light split into two beams, which can be regarded as secondary sources radiating light into the waveguide array. As a result, many light beams can be generated in the array by the coupling among the waveguides, and the interference of these light beams after passing the system leads to directional emission. Additionally, the directional emission is greatly affected by the beam distribution on the exit plane of the system. Once the main light beams are formed on the exit plane of the system by modulating the system size, steady beaming effect can be obtained in the horizontal direction.     

Sub-terahertz on-off switch based on a two-dimensional photonic crystal infiltrated by liquid crystals

A sub-terahertz switch is realized by infiltration of a two-dimensional photonic crystal (PC) with the liquid crystal 5CB. On-off switching is based on a shift of the bandgap of the PC by applying an external electric field which rotates the 5CB molecules. We confirm theoretically and experimentally that rotating the optical axis of the 5CB molecules considerably affects the transmission of the electromagnetic waves of TM polarization in the stop band. The effect can be used for on-off switching of the electromagnetic waves in the sub-terahertz range. Experimentally we demonstrate an extinction ratio of 13.3 dB at 91 GHz.     

Modulation of focus using photonic crystal waveguide

We study theoretically that a photonic crystal waveguide with modulated output surface can focus electromagnetic wave just like a lens. The characters of the focus are sensitive to the surface morphology and can be modulated by adjusting the parameters. Two methods are proposed to modify the focus, and an interesting off-axis focus is found in an asymmetrical structure.     

Beaming effect from increased-index photonic crystal waveguides

We study the beaming effect of light for the case of increased-index photonic crystal (PhC) waveguides, formed through the omission of low-dielectric media in the waveguide region. We employ the finite-difference time-domain numerical method for characterizing the beaming effect and determining the mechanisms of loss and the overall efficiency of the directional emission. We find that, while this type of PhC waveguide is capable of producing a highly collimated emission as was demonstrated experimentally, the inherent characteristics of the structure result in a restrictively low efficiency in the coupling of light into the collimated beam of light.     

Lamellar model of the left-handed metamaterials composed of metallic split-ring resonators and wires

Left-handed materials composed of split ring resonators (SRRs) and wires are investigated in the viewpoint of lamellar composite with epsilon-negative (ENG) and mu-negative (MNG) materials staked alternatively. Several configurations of the SRR-wire metamaterial are numerically simulated to confirm its left-handed response as an analogy to the ENG-MNG lamellar model.     

Amphoteric-like refraction in a two-dimensional photonic crystal

High-index contrast photonic crystals possess an intricate photonic band structure that is responsible for surprising phenomena as the surperprism effect, self-collimation, power splitting or negative refraction. Recently, it was reported that at the interface between an isotropic medium and a uniaxial crystal (or between two uniaxial crystals) a phenomenon known as amphoteric refraction, that is, positive as well as negative refraction, can take place. By means of a equifrequency contours analysis and finite-difference time-domain simulations, we show that a two dimensional photonic crystal can also present amphoteric refraction by properly choosing the lattice orientation and the termination. However, total transmission is difficult to achieve because a Bloch mode is excited inside the photonic crystal and the coupling efficiency from this mode to an external plane wave is lower than one.     

Effects of Parameter Modulation on Near-Field Imaging in Photonic Crystal Consisting of Alternately Left-Handed Material and Right-Handed Material

By means of the transfer-matrix method, the effects of parameter modulation on the quality of near-field imaging in one-dimensional photonic crystal consisting of alternately left-handed material and right-handed material are investigated. Based on analyses of the recovery rate and phase shift, the results show that the imaging quality is not obviously affected by the minor changes of layer thickness. In addition, by modulating the material parameters of the left-handed material, it is found that for both the real part and the imaginary part, the system is more sensitive to the permeability than the permittivity for the TE wave. For the TM wave, it is reverse. These properties are very useful to fabricate left-handed material photonic crystals in practice.     

Extended plane-wave-based transfer-matrix approach to simulating dispersive photonic crystals

It has been difficult to compute the band structures and transmission spectra for photonic crystals (PCs) with dispersive components included in the periodic units. Here we show that by using an extended plane-wave-based transfer-matrix method, we are able to formulate the problem for computing optical properties of dispersive PCs, including magnetic and left-handed PCs. This approach is very general, since it can treat PCs with arbitrary Bravais lattice composed of materials with arbitrary dielectric permittivities and magnetic permeabilities. Combined with the supercell method, this method can further simulate defective PCs such as PC-based waveguides and microcavities.     

Optical properties of one-dimensional photonic crystals containing graded materials

The optical properties of an one-dimensional photonic crystal containing graded materials are studied theoretically. The graded layers have space dispersive permittivity and magnetic permeability which vary along the direction perpendicular to the surface of the layer. The gradation profiles of permittivity are studied in detail. We show that the structure possesses forbidden band gaps in its transmission spectra and the gradation profiles of permittivity affect the band gaps significantly. For the exponential gradation profile ε₁(x) = α e^βx, the number of the band gaps increases and the total frequency region corresponding to the gaps becomes large with increasing parameter β. On the other hand, the position of band gaps can be changed by the adjustment of the gradation profiles even if possessing same volume-average permittivity in the graded layers. Therefore, we can achieve suitable photonic band gaps by choosing gradation profiles of permittivity.