2D Photonic Crystal Waveguide Research Articles

Propagation loss in a two-dimensional triangular photonic crystal waveguide

By means of a plane-wave-based transfer-matrix method, we present an extensive study of propagation loss in two-dimensional (2D) photonic crystal waveguides with limited cladding wall thickness. We examine the dependence of propagation loss on both the propagation direction and the waveguide wall thickness. It is shown that the propagation loss is a function of excitation frequency, wall thickness and waveguide outermost surface morphology. The conclusion that the propagation loss essentially decays exponentially with respect to the cladding wall thickness of a waveguide is valid only to a certain degree. In addition, we find that the propagation loss exhibit very complex behavior with respect to the excitation frequency.

Efficient coupling from dielectric rib waveguide to two-dimensional photonic crystal waveguide

An efficient adiabatic coupling is presented in this paper for coupling light between rib dielectric waveguide and 2D photonic crystal waveguide (PCW). Using planar wave expand (PWE) method and FDTD method, the linear and nonlinear taper profiles are compared. Following with these, some widths of the entrance of the taper are compared and the best width is given. Simulation result have proved that transmission ratio above 95% can be obtained in a wider frequency range by usin g a cosine taper profile than line taper profile.

Analysis of polarization plane rotation characteristic in 2D photonic crystal waveguide with chiral medium by condensed node spatial network

Using the photonic band gap in photonic crystals, the fundamental waveguide structures for the light wavelength range have been developed. Based on the fine structure of these many functional devices have been proposed by analytical or numerical simulation methods and the experiments of trial manufacture. In this paper, the treatment of chiral dielectric in the Condensed Node Spatial Network for the vector potential is explained, and we show the polarization plane rotation property in air-hole and pillar type photonic crystal waveguide structures with the chiral medium substrate. Then, we show the fundamental advantage of the air-hole type photonic crystal waveguide structure in application to a mode converter. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(1): 7–14, 2005; Published online in Wiley InterScience (www.interscience. wiley.com). DOI 10.1002/eej.20098

Coupling analysis of heterogeneous integrated InP based photonic crystal triangular lattice band-edge lasers and silicon waveguides

In recent years, many groups have envisioned the possibility of integrating optical and electronic devices in a single chip. In this paper, we study the integration of a photonic crystal laser fabricated in InP with a silicon passive waveguide. The coupling of energy between a 2D photonic crystal (PhC) triangular lattice band-edge laser and waveguide positioned underneath is analyzed in this paper. We show that a 40% coupling could be achieved provided the distance between the laser and the waveguide is carefully adjusted. A general description of the fabrication process used to realize these devices is also included in this paper.

Ultralow refractive index substrates–a base for photonic crystal slab waveguides

Out of plane radiation losses in two-dimensional (2D) photonic crystal (PC) waveguides occur due to a lack of total internal reflection at the core-substrate∕superstrate boundaries. In order to minimize these losses, either a high vertical refractive index contrast or deep etching into the substrate is required [G. Boettger, C. Liguda, M. Schmidt, and M. Eich, Appl. Phys. Lett. 81, 2517 (2002)]. The maximum vertical contrast is achieved in air bridge type PC waveguides, which are inherently fragile. In this article, we introduce a concept which combines the advantages of a high vertical index contrast of an air bridge with those of a solid substrate. This approach consists of mesoporous silica as substrate material with an ultralow refractive index (n=1.14 at 1.3μm), close to that of air. Finite 2DPC line defect resonators consisting of an optical polymer as core and mesoporous silica as substrate were fabricated. Compared to ordinary substrates with higher refractive indices like silica or amorphous Teflon [C. Liguda, G. Boettger, A. Kuligk, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, Appl. Phy. Lett. 78, 2434 (2001)], measurements show significantly increased transmission at the resonance wavelength and virtually no losses on the sensitive air band side.

Towards nano-waveguides

We propose a hybrid type of photonic crystal waveguide (PCW) structure, in which two-dimensional (2D) PCW is embedded in a two one-dimensional (1D) PCW. This rather new PCW structure should be identical to a full three-dimensional PCW in its functionality, but its fabrication is much simpler. Toward the realization of such an amenable PCW structure, an epitaxially grown GaAs/AlAs multilayer structure was successfully converted to an omnidirectional reflector, suitable for the 1D photonic crystal structure in the hybrid PCW. In terms of fabricating 2D-PCWs, we took a rather new approach instead of conventional electron-beam lithography. An air-bridge type of thin film Si 2D-PCW was fabricated using a combined technique of holography and photolithography. Optical characterizations revealed that the propagation loss of the waveguide fabricated such is comparable to those of e-beam generating PCWs in the literature.

Analysis of fundamental property of 2D photonic crystal optical waveguide with various medium conditions by condensed node spatial network

AbstractPhotonic crystals have a stopband characteristic (photonic bandgap: PBG) in which the light in a specific wavelength band is strongly attenuated. This structure is expected to exhibit the possibility of fine‐structure devices with sharp bends on the order of a wavelength that cannot be realized by weakly guided waves such as those in an optical fiber and a slab waveguide. However, significant difficulties are expected for their design and fabrication. Therefore, understanding and prediction by simulation are indispensable. To date, many analyses have been carried out by the FDTD method and the BPM method. In particular, for the fabrication of functional optical‐circuit devices, it is necessary to carry out a global analysis of the photonic crystal optical waveguide, including dielectric materials with dispersion and nonlinear effects. In this paper, the fundamental properties of photonic crystal optical waveguides containing various media are analyzed by means of the special feature of treating the medium condition in the condensed node spatial network method. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 2, 85(5): 10–20, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjb.10018

Single mode lasers based on monolithic integration of ridge waveguides with 2D photonic crystal waveguides

The monolithic combination of active light sources with photonic crystal (PC) waveguide components is a key building block for future highly integrated photonic circuits. We demonstrate the coupling of light from an InGaAs/AlGaAs ridge waveguide laser to a monolithically integrated 2D PC waveguide. The PC guide is formed by removing three or five rows in a triangular lattice of air rods etched into the semiconductor. A tapered ridge waveguide geometry is demonstrated to improve coupling efficiency, so that maximum output powers of up to 10 mW from the PC waveguide are achieved. The resulting coupled cavity laser shows single mode emission with side mode suppression ratios > 35 dB over a broad range of injection currents.

Numerical analysis of propagation and impedance matching in 2D photonic crystal waveguides with finite length

A novel way of approaching wave propagation in two-dimensional (2-D) photonic crystal guides with finite length is presented. It is shown that the main propagation features can be captured by borrowing simple concepts of propagation in transmission lines and combining them with other concepts taken from the theory of periodic structures.

Design and optimization of 2D photonic crystal waveguides based on silicon

The existence and properties of photonic band gaps was investigated for a square lattice of dielectric cylinders in air. Band structure calculations were performed using the transfer matrix method as function of the dielectric constant of the cylinders and the cylinder radius-to-pitch ratio r/a. It was found that band gaps exist only for transverse magnetic polarization for a dielectric contrast larger then 3.8 (index contrast >1.95). The optimum r/a ratio is 0.25 for the smallest index contrast. For silicon cylinders (n = 3.45) the widest gap is observed for r/a = 0.18. Band structure calculations as function of r/a show that up to four gaps open for the silicon structure. The effective index was obtained from the band structure calculations and compared with Maxwell–Garnett effective medium theory. Using the band structure calculations we obtained design parameters for silicon based photonic crystal waveguides. The possibility and limitations of amorphous silicon, silicon germanium and silicon-on-insulator structures to achieve index guiding in the third dimension is discussed.

Coupling and decoupling of electromagnetic waves in parallel 2D photonic crystal waveguides

The behavior of two nearby straight photonic crystal waveguides is analyzed. It is shown that the two guides, considered as a single system, may realize a very efficient wavelength selective directional coupler, that may be used as a channel interleaver in a WDM communications system. In addition, we also show that, by properly designing the geometry of the dielectric region between the guide cores, waveguide decoupling can be obtained. Necessary conditions for this feature to be obtained are analytically derived, and an electromagnetic explanation of the decoupling process is given.

Long-range interaction and nonlinear localized modes in photonic crystal waveguides

We develop the theory of nonlinear localized modes (intrinsic localized modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods embedded into an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a nonlinear lattice model with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided mode that are also localized in the waveguide direction, and describe their unique properties, including bistability.

Demonstration of highly efficient waveguiding in a photonic crystal slab at the 15-µm wavelength

Highly efficient transmission of 1.5-microm light in a two-dimensional (2D) photonic crystal slab waveguide is experimentally demonstrated. Light waves are shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism. At certain wavelength ranges, complete transmission is observed, suggesting lossless guiding along this photonic one-dimensional conduction channel.

Bent laser cavity based on 2D photonic crystalwaveguide

The authors have successfully fabricated a bent ridge-waveguide laser cavity on an InGaAs/AlGaAs GRINSCH laser structure using a 2D photonic crystal to reduce the radiation loss. A clear dependence of CW laser performance and near field behaviour on the period of the photonic crystal is demonstrated.