Tunable Goos-Hänchen shift for self-collimated beams in two-dimensional photonic crystals

We present finite-difference time-domain studies of the Goos-Hänchen effect observed at the reflection of a self-collimated beam from the surface of a two-dimensional photonic crystal. We describe a method of tuning the shift of the reflected beam in photonic crystals through the modification of the surface, first structurally, as a change in the radius of the surface rods, and then all-optically, with the addition of nonlinear material to the surface layer. We demonstrate all-optical tunability and intensity-dependent control of the beam shift.     

Wavelength demultiplexers based on multimode interference effect in photonic crystals

We present a compact photonic crystal wavelength demultiplexing device based on multimode interference effect. The finite-difference time-domain method is used to verify and analyze the characteristics of the device. Results show the demultiplexing function of the device can be obtained with greater than 20 dB isolation ratio and about 20 nm bandwidth at both wavelength bands.     

Properties of defect modes in one-dimensional photonic crystals containing a graded defect layer

The properties of defect modes in one-dimensional photonic crystals (PCs) containing a graded defect layer are studied theoretically. The relative permittivity and magnetic permeability of the graded defect layer vary continuously along the direction perpendicular to the surface of the layer. The effect of the linear gradation profiles of the relative permittivity and permeability are studied in detail. It is shown that the defect modes appear inside the forbidden band gaps in its transmission spectra and the gradation profiles of the relative permittivity and permeability affect the defect modes significantly. By changing the gradation parameters, the intensity and position of the defect modes can be tuned. Therefore, introducing a graded defect layer in one-dimensional PCs provides possible mechanism for tuning the defect modes. This may be useful in the design of channeled filters.     

Self-collimation and beam splitting in low-index photonic crystals

We study self-collimation and beam splitting in low-refractive-index photonic crystals created within chalcogenide glass. We propose a beam splitter structure that allows direct experimental verification of photonic-crystal effects at optical wavelengths in a straightforward and definitive manner. The beam splitter provides angular separation of 90° using a highly compact spatial footprint, thus delivering direct application in highly integrated photonic devices.     

Tunable band gaps in electro-optical photonic bi-oriented crystals

Electrically induced birefringence is studied in photonic bi-oriented crystals in terms of molding lightflow in optical devices. In photonic bi-oriented crystals, misorientation of dielectric anisotropic grains results in a dielectric contrast at the grain boundaries. The translational periodicity of the optical constants depends upon a regular network of twisted dielectrics. Due to the anisotropy of the bicrystalline structure the direction of light propagation determines the dielectric contrast at the grain boundaries. In a specific crystallographic arrangement the optical properties of the bi-oriented crystal can be tuned by the electro-optical effect: the periodic dielectric contrast is electrically induced and photonic bandgaps are generated by applying external electric fields. The geometrical requirements for tunable photonic bicrystals are evaluated based on materials employed for electro-optical applications. Tunable photonic bi-oriented crystals may be candidates for fast optical switches, modulators and multiplexers in the optical communication network. Received: 5 July 2001 / Revised version: 3 August 2001 / Published online: 15 October 2001     

Superbending effect in two-dimensional graded photonic crystals

We study the superbending effect in a two-dimensional graded photonic crystal (GPC) for both TE and TM modes. We show that the lateral beam shift is extremely sensitive to the wavelength for the TM mode but not TE mode, indicating the potential in designing some special superbending devices, for example, TE/TM splitter and polarization-indifference waveguide at prescribed wavelengths.     

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.     

Photonic band gap effect in one-dimensional plasma dielectric photonic crystals

Propagation of electromagnetic waves in one-dimensional plasma dielectric photonic crystals, the superlattice structure consisting of alternating plasma and dielectric materials, is studied theoretically using transfer matrix method. Numerical calculation is presented for plasma-air finite and infinite periodic structures. The results of photonic band gap characteristics are discussed in terms of plasma density, plasma width, and number of unit cells (N).     

The effect of etching interfacial layers on the absolute photonic band gap in two-dimensional photonic crystals

The photonic band structures of two-dimensional (2D) photonic crystals with etched interfacial layers between air rods and the background dielectric is studied theoretically. The effect of etching interfacial layers on absolute photonic band gap (PBG) is analyzed quantitatively. Numerical calculations are carried out based on Maxwell's equations and the plane-wave expansion method. It is shown that the physical property of interfacial layers influence the absolute PBG, and the existence of interfacial layers cannot enlarge the largest absolute PBG of an ideal case without interfacial layers.     

Band-structure determination for finite 3-D photonic crystals

The partial band structure from a finite photonic crystal is determined using a model based on light diffraction and the transfer-matrix formalism. The predictions from such a model are compared to an experimental measurement of the bands in the LU direction of a face centered cubic colloidal crystal. Then, both the theoretical predictions and the experimental measurements are compared with the usual band-structure calculation based on a plane-wave expansion with perfectly periodic boundary conditions. As in measurements performed in the past, discrepancies between the predictions of this later model and the experimentally determined bands are observed. On the contrary, using the model presented based on light propagation through a finite crystal, where no periodicity is imposed in the direction perpendicular to any of the set of planes considered to determine a specific branch of the band structure, we found a very good agreement between the experimentally determined and the predicted bandwidths.     

Quantitative analysis of subdiffractive light propagation in photonic crystals

We present a qualitative study of the subdiffractive light beam propagation in photonic crystals, based on the theoretical analysis of full Maxwell equation system beyond the slowly varying envelope and paraxial approximations. We calculate the zero diffraction curve in the parameter space, we calculate the weak asymptotical broadening (spreading in transverse direction), and we also analyze the dependence of subdiffractive propagation on the polarization orientation (both for TM and TE polarization).     

Emissions of Photonic Crystal Waveguides with Discretely Modulated Surfaces

Transmission properties of photonic crystal （PC） waveguides with discretely modulated exit surfaces are investigated numerically using the finite-difference time-domain （FDTD） method. Unlike the case of periodically modulated surfaces, where the transmission beam tends to be a single and directional beam, when the exit surfaces are modulated only at several discrete points, the emission power tends to split into multiple and directional beams. We explain this phenomenon using a multiple point source interference model. Based on these results, we propose a 1-to-N beam splitter, and numerically realized high efficiency coupling between a PC sub-wavelength waveguide and three traditional dielectric waveguides with a total efficiency larger than 92%. This simple, easy fabrication, and controllable mechanism may find more potential applications in integrated optical circuits.     

Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers

We study the shift of a long period grating’s resonance wavelength with UV induced refractive index changes in an all-solid photonic bandgap fiber. A long period grating is mechanically imprinted in an all-solid photonic bandgap fiber with Germanium doped silica high-index rods in a lower-index silica background. The index of the high-index rods is modified through UV exposure, and we observe that the long period grating’s resonance shifts with the bandgaps. With a sensitivity of 21,000 nanometers per refractive index unit and a 8.8 nm resonance width changes of refractive index of 3 × 10⁻⁶ are in principle detectable     

A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals

We investigate one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization directions. Significant enhancement of second harmonic generation (SHG) is observed from numerical simulations when the frequency of fundamental wave is aimed at the photonic band edge. We devise the model structure with optimal configuration of the polarization directions of the ferroelectric domains in terms of simulated annealing algorithm. The conversion efficiencies of the ‘forward’ and ‘backward’ SHGs can be engineered.     

Superprism effect in 1D photonic crystal

It is shown that superprism effect can be observed not only in 2D and 3D photonic crystal but also in 1D photonic crystal. To observe the effect a diffraction grating should be put on the top of the 1D PC. It is shown that the band gap more dramatically appears in 1D PC than in 2D PC. This effect makes all PBG effects including superprism effect more pronounced and also weakens the influence of losses.     

Wavelet method for computing band diagrams of 2D photonic crystals

A wavelet method is applied for the first time to the computation of band diagrams of photonic crystals (PhCs). The wavelet algorithm is described. Its numerical implementation is validated in the case of emblematic two-dimensional triangular and square lattice PhCs. Although these examples do not emphasize the full power of wavelet methods, the number of wavelets needed to achieve a prescribed accuracy is already shown to be orders of magnitude smaller than the number of waves used in the traditional plane wave method. Further extension to more complex photonic structures is discussed.     

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.     

Flexible all-plastic mirrors for the THz range

We present a simple and cheap approach to fabricate large-area stop-band filters and mirrors for the THz range. This approach extends the well-known concept of dielectric mirrors to the far infrared. We use alternating layers of different polymer materials with a typical thickness of several tens of micrometers to build a flexible all-plastic mirror. The structures are characterized by THz time-domain spectroscopy. The experimental results are in good agreement with transfer-matrix simulations. Received: 28 September 2001 / Accepted: 4 October 2001 / Published online: 20 December 2001     

The Sommerfeld precursor in photonic crystals

We calculate the Sommerfeld precursor that results after transmission of a generic electromagnetic plane wave pulse with transverse electric polarization, through a one-dimensional rectangular N-layer photonic crystal with two slabs per layer. The shape of this precursor equals the shape of the precursor that would result from transmission through a homogeneous medium. However, amplitude and period of the precursor are now influenced by the spatial average of the plasma frequency squared instead of the plasma frequency squared for the homogeneous case.     

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.