Triangular Lattice Photonic Crystal Slab Research Articles

Multichannel W3 Y-branch filter in a two dimensional triangular-lattice photonic crystal slab

We demonstrate the design, fabrication and characterization of a highly efficient multichannel W3 Y-branch filter in a two dimensional triangular-lattice photonic crystal slab. The coupling properties between high-order waveguide modes and fundamental resonant modes are investigated. By finely adjusting the size of resonant cavities, four higher-order mode channels with different output wavelengths are experimentally realized, which is in agreement with the theoretical simulations. The results show that this kind of filter may be useful in optical integrated circuits with high coupling and transmission efficiency.

Large mode-volume, large beta, photonic crystal laser resonator

We propose an optical resonator formed from the coupling of 13, L2 defects in a triangular-lattice photonic crystal slab. Using a tight-binding formalism, we optimized the coupled-defect cavity design to obtain a resonator with predicted single-mode operation, a mode volume five times that of an L2-cavity mode and a beta factor of 0.39. The results are confirmed using finite-difference time domain simulations. This resonator is very promising for use as a single mode photonic crystal vertical-cavity surface-emitting laser with high saturation output power compared to a laser consisting of one of the single-defect cavities.

Design of high-Q polystyrene nonlinear cavity for ultrafast all-optical switching in mid-infrared photonic crystal slabs with cavity-waveguide structure

In this study, we design a nonlinear cavity with ultrafast response speed material in photonic crystal slabs for all-optical switching. We consider triangular lattice photonic crystal slab made from air holes in anisotropic Tellurium background which is on top of Teflon substrate. The cavity itself is then created by enlarging one of the air holes and infiltrating it with polystyrene. Optimization of structural parameters yields a single mode cavity with quality factor of Q=2.5×104, by using the three-dimensional finite-difference time-domain (FDTD) simulation and filter diagonalization approach. This shows great enhancement compared with previous studies in which organic polymer materials have been used. In order to study the coupling characteristic of cavity mode and waveguides, the nonlinear cavity is placed between two waveguides, symmetrically. At the end, we used the FDTD method to investigate shift magnitude of cavity mode resonance frequency under pump light. The designed structure can be helpful to achieve extremely fast response speed in all-optical switching devices with high efficiency in the mid-infrared wavelength range.

Improving unrestricted imaging quality of a triangular lattice photonic crystal slab by modifying surface configuration

We propose a photonic crystal (PC) structure only by replacing square lattice [Luo et al. (2002) [12]] with triangular lattice to obtain an unrestricted imaging. Equal-frequency contours (EFCs) analysis shows that this triangular lattice two-dimensional PC exhibits an effective isotropic refractive index n eff=−1 at a normalized frequency ω=0.291×2 πc/ a. Imaging quality of this triangular lattice PC slab involving both power intensity and full-width at half-maximum intensity of the image is studied using the finite-difference time-domain (FDTD) simulation. In order to achieve a high-quality image, an appropriate surface termination is chosen. In addition, by adjusting the surface air-hole radius of the PC slab, the imaging quality can be further improved. Coupled-mode theory analysis shows that the optimized surface termination and the adjusted surface air-hole can excite two kinds of surface modes that can couple with the Bloch wave in the PC. With the help of these surface modes, both the intensity of image and the super-resolution capacity of this triangular lattice PC slab can be improved greatly.

Multichannel filters via Γ-M and Γ-K waveguide coupling in two-dimensional triangular-lattice photonic crystal slabs

We demonstrate the design, fabrication, and characterization of a multichannel filter in a two-dimensional triangular-lattice photonic crystal slab. The output signal channel, which directs in the Γ-M crystalline direction, is orthogonal to the input signal channel that directs in the Γ-K crystalline direction. In each channel, the filtering function is guaranteed by the indirect resonant coupling between the waveguide and the cavity. Four resonant cavities with different sizes provide the mechanism of finely tuning the output wavelength. Our experimental results are in good agreement with simulations.

Finite-Difference Time Domain Method for Nonorthogonal Unit-Cell Two-Dimensional Photonic Crystals

A finite-difference time-domain (FDTD) method based on a regular Cartesian Yee's lattice is developed for calculating the dispersion band diagram of a 2-D photonic crystal. Unlike methods that require auxiliary difference equations or nonorthogonal grid schemes, our method uses the standard central-difference equations and can be easily implemented in a parallel computing environment. The application of the periodic boundary condition on an angled boundary involves a split-field formulation of Maxwell's equations. We show that the method can be applied for photonic crystals of both orthogonal and nonorthogonal unit cells. Complete and accurate bandgap information is obtained by using this FDTD approach. Numerical results for 2-D TE/TM modes in triangular lattice photonic crystals are in excellent agreement with the results from 2-D plane wave expansion method. For a triangular lattice photonic crystal slab, the dispersion relation is calculated by a 3-D FDTD method similarly formulated. The result agrees well with the 3-D finite-element method solution. The calculations also show that the 2-D simulation using an effective index approximation can result in considerable error for higher bands.

Multiwavelength ultralow-threshold lasing in quantum dot photonic crystal microcavities

We demonstrate multiwavelength lasing of resonant modes in linear (L3) microcavities in a triangular-lattice 2D photonic crystal (PC) slab. The broad spontaneous emission spectrum from coupled quantum dots, modified by the PC microcavity, is studied as a function of the intensity of incident optical excitation. We observe lasing with an ultralow-threshold power of approximately 600 nW and an output efficiency of approximately 3% at threshold. Two other resonant modes exhibit weaker turnon characteristics and thresholds of approximately 2.5 and 200 microW, respectively.

Photonic band tuning in two-dimensional photonic crystal slab waveguides by atomic layer deposition

The photonic bands of two-dimensional (2D) triangular lattice photonic crystal Si slab waveguides were statically tuned using low temperature atomic layer deposition (ALD) of TiO2. Angular dependent reflectance measurements of bare and coated devices were well fitted by three-dimensional finite-difference time-domain calculations. The technique not only allows the physics of photonic band effects in 2D photonic crystals to be systematically studied but also demonstrates large static tuning and precise fine-scale control over band frequency and dispersion, with a frequency tuning range of 12% and precision of 0.005% per ALD cycle. Band tuning to achieve zero group velocity is demonstrated.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Padé approximation. The decaying constant β of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity vg as β=ω/(2Qvg). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 103 to 10−4cm−1 can be reliably obtained from 8×103-item FDTD output with the FDTD computing time of 0.386ps. And at most 1ps is required for the mode with the Q-factor of 4×1011 and the decaying rate of 10−7cm−1. In the triangular-lattice photonic crystal slab, a 104-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5×108 and the decaying rate of 0.05cm−1.

Channel drop filters using resonant tunneling processes in two-dimensional triangular lattice photonic crystal slabs

We present a channel drop filter by using channel drop tunneling processes in a two-dimensional triangular lattice photonic crystal slab. The channel drop filter is composed of two waveguides and two donor-type three-missing-holes cavities. At resonance, the power transferred to the drop waveguide and the power remaining in the bus are found to be about 61% and 5%, respectively. In order to improve the filter response, the out-of-plane quality factor must be much higher than the in-plane quality factor.

Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode

Coupling characteristics between the single-cell hexapole mode and the triangular-lattice photonic crystal slab waveguide mode is studied by the finite-difference time-domain method. The single-cell hexapole mode has a high quality factor (Q) of 3.3Chi106 and a small modal volume of 1.18(lambda/n)3. Based on the symmetry, three representative types of coupling geometries (shoulder-couple, butt-couple and side-couple structures) are selected and tested. The coupling efficiency shows strong dependence on the transverse overlap of the cavity mode and the waveguide mode over the region of the waveguide. The shoulder-couple structure shows best coupling characteristics among three tested structures. For example, two shouldercouple waveguides and a hexapole cavity result in a high performance resonant-tunneling-filter with Q of 9.7Chi105 and transmittance of 0.48. In the side-couple structure, the coupling strength is much weaker than that of the shoulder-couple structure because of the poor spatial overlap between the mode profiles. In the direct-couple structure, the energy transfer from the cavity to the waveguide is prohibited because of the symmetry mismatch and no coupling is observed.

Diffractionless optical networking in an inverse opal photonic band gap micro-chip

We present a design for a photonic crystal (PC) all-optical micro-chip based on a three-dimensional (3D) inverse opal heterostructure intercalated with a two-dimensional (2D) triangular lattice photonic crystal slab. Within the 2D micro-chip layer, we demonstrate single-mode (diffractionless) waveguiding of light in air, throughout a bandwidth of more than 70 nm near 1.55 μm. This suggests that inverse opal photonic band gap (PBG) materials can facilitate on-chip optical networking functions over the telecommunication frequency band used in current-day optical fibers.