Woo Jun Kim

Two-dimensional photonic crystal Mach–Zehnder interferometers

Mach-Zehnder interferometers were fabricated from suspended membrane photonic crystal waveguides. Transmission spectra were measured and device operation was shown to be in agreement with theoretical predictions.

Quality factors in single-defect photonic-crystal lasers with asymmetric cladding layers

We present quality factors of single-defect photonic-crystal resonant cavities with asymmetric cladding layers. The resonators studied here are dielectric slabs patterned with two-dimensional photonic crystals on a sapphire substrate. Three-dimensional finite-element and finite-difference time-domain routines were used to analyze the electromagnetic properties of these cavities. We observe that high quality factors (∼800) can be obtained in these cavities for reasonable structures with thick enough dielectric slabs. This work was motivated by the need to place photonic-crystal resonators on a substrate to improve heat dissipation in photonic-crystal lasers.

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 Yees 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 Maxwells 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.

Propagation Loss of Line-Defect Photonic Crystal Slab Waveguides

Photonic crystal slab waveguides are created by inserting a linear defect in two-dimensional (2-D) periodic dielectric structures of finite height. Photonic crystals provide 2-D in-plane bandgaps through which light cannot propagate, however, the fact that the waveguide modes must be index-confined in the vertical direction implies that the propagation loss is strongly dependent on the out-of-plane radiation loss. We present a fully three-dimensional finite-difference time-domain numerical model for calculating the out-of-plane radiation loss in photonic crystal slab waveguides. The propagation loss of the single-line defect waveguide in 2-D triangular lattice photonic crystals is calculated for suspended membranes, oxidized lower claddings, and deeply etched structures. The results show that low-loss waveguides are achievable for sufficiently suspended membranes and oxidized lower cladding structures. The roles of the photonic crystal in out-of-plane loss of the waveguide modes are further analyzed. It is predicted that the out-of-plane radiation loss can be reduced by shifting one side of the photonic crystal cladding by one-half period with respect to the other sides along the propagation direction

Dispersion characteristics of photonic crystal coupled resonator optical waveguides

We investigated group velocities and group velocity dispersion characteristics of photonic crystal waveguides and coupled resonator optical waveguides(CROWs). In photonic circuits comprised of the linear defect waveguides, the insertion of the CROW section suppresses energy flow due to its highly dispersive characteristics. We analyze the change in the group velocity and the group velocity dispersion by varying the radius of the holes in the waveguide channel. Properly designed CROW sections provide a wide range of control in the group velocity and positive/negative group velocity dispersion. They can be used as delay lines or dispersion compensators in photonic integrated circuits comprised of linear defect photonic crystal waveguides.

Calculated out-of-plane transmission loss for photonic-crystal slab waveguides

A fully three-dimensional finite-difference time domain numerical model is presented for calculating the out-of-plane radiation loss in photonic-crystal slab waveguides. The propagation loss of a single-line defect waveguide in triangular-lattice photonic crystals is calculated for suspended-membrane, oxidized-lower-cladding, and deeply etched structures. The results show that low-loss waveguides are achievable for sufficiently suspended membranes and oxidized-lower-cladding structures.

Experimental characterization of the reflectance of 60° waveguide bends in photonic crystal waveguides

Photonic crystal waveguides with two 60° bends were fabricated in an InGaAsP∕InP suspended membrane geometry. The transmission spectrum was measured and the reflectance of the 60° bend was evaluated from Fabry–Perot oscillations using Fourier analysis. It is shown that the reflectance agrees well with the results of a finite element method simulation.

Quality factors in single defect photonic crystal lasers with asymmetric cladding layers

We present calculations that allow the design of two-dimensional photonic crystal resonant cavities in dielectric slabs bonded to a sapphire substrate. Finite-difference time-domain (FDTD) calculations of quality factors in two-dimensional photonic crystal membranes on a sapphire substrate were performed. We considered a triangular lattice with a single missing hole, and it is the Q of the doubly-degenerate resonant mode associated with this missing hole that we were concerned with. The Q of the cavity was obtained by multiplying the resonant frequency, which was obtained from a Fourier transform of the field, by the energy stored in the cavity and then dividing by the power lost out of the cavity.

Photonic Crystal Devices

We report on two-dimensional photonic crystal devices. We will discuss the properties of photonic crystal sources and passive waveguide components. This will include a discussion of device design and modeling as well as experimental results.

Experimental characterization of the reflectance of 60-degree waveguide bends in photonic crystal waveguides

Photonic crystal waveguide bends were fabricated and characterized. Good agreement was obtained between the numerical predictions of the transmission spectra and the experimental observations.