_{2}-GaAs annular photonic crystals

^{1,a)}, Hong Wu

^{1}, Wei Jia

^{1,2}and Xiang-Yin Li

^{1}

### Abstract

We systematically investigated the negative refraction effect for both TM and TE polarization modes in SiO_{2}-GaAs annular photonic crystals with triangular lattice. It was found that, in comparison with normal triangular-lattice air-holes photonic crystals, the annular photonic crystals have much lower and flatter band structures, which are quite beneficial to the formation of convex equifrequency surfaces for both polarizations. Further analyses on equifrequency surfaces and the electric field distribution of annular photonic crystals with different parameters have not only first demonstrated the possibility of polarization-independent negative refraction effect in annular photonic crystals, but also revealed some important laws to control the working frequency and performance of this remarkable effect.

This work was supported by NUST research funding (No. 2010ZYTS059 and No. AE88030) and the Natural Science Foundation of Jiangsu Province (No. BK2010483).

I. INTRODUCTION

II. MODEL AND METHODS

III. THE POSSIBILITY OF POLARIZATION-INDEPENDENT NEGATIVE REFRACTIVE IN NORMAL AIR-HOLES PCS

IV. THE POSSIBILITY OF POLARIZATION-INDEPENDENT NEGATIVE REFRACTIVE IN APCs

V. SUMMARY

### Key Topics

- Negative index materials
- 34.0
- Vortex pinning
- 21.0
- Band structure
- 12.0
- Dielectrics
- 12.0
- Polarization
- 12.0

## Figures

(Color online) Schematic diagram of the triangular-lattice APC in X-Y plane. Dielectric cylinders (refractive index *n* _{2}) with radius *r* _{2} are centered in air holes (*n* _{1} = 1), with radius *r* _{1} based on dielectric background (refractive index *n* _{0}). *a* is the lattice constant defined as the distance between the centers of two adjacent cylinders or air holes.

(Color online) Schematic diagram of the triangular-lattice APC in X-Y plane. Dielectric cylinders (refractive index *n* _{2}) with radius *r* _{2} are centered in air holes (*n* _{1} = 1), with radius *r* _{1} based on dielectric background (refractive index *n* _{0}). *a* is the lattice constant defined as the distance between the centers of two adjacent cylinders or air holes.

(Color online) On condition that *n _{eff} * = −1, the normalized frequency for TE polarization (

*ω*

_{TE}), TM polarization (

*ω*

_{TM}), and the frequency difference Δ

*ω*vs air-holes radius

*r*

_{1}in normal triangular-lattice air-holes PCs when

*r*

_{2}= 0 and

*n*

_{0}= 1.52. The inset shows the enlarged view of scanned curve for Δ

*ω*.

(Color online) On condition that *n _{eff} * = −1, the normalized frequency for TE polarization (

*ω*

_{TE}), TM polarization (

*ω*

_{TM}), and the frequency difference Δ

*ω*vs air-holes radius

*r*

_{1}in normal triangular-lattice air-holes PCs when

*r*

_{2}= 0 and

*n*

_{0}= 1.52. The inset shows the enlarged view of scanned curve for Δ

*ω*.

(Color online) The EFSs [(a)-(c)] and corresponding FDTD simulation of electric-field distribution [(d)-(f)] for normal triangular-lattice air-holes PCs with different values of *r* _{1} when *r* _{2} = 0 and *n* _{0} = 1.52. In each FDTD simulation, a Gaussian point source with width of 0.5*a* is placed 0.5*a* away from the PC, which has a dimension of . In Fig. 3(b), for a given incident wave along direction , and represent the corresponding refractive direction for TE mode and TM mode, respectively.

(Color online) The EFSs [(a)-(c)] and corresponding FDTD simulation of electric-field distribution [(d)-(f)] for normal triangular-lattice air-holes PCs with different values of *r* _{1} when *r* _{2} = 0 and *n* _{0} = 1.52. In each FDTD simulation, a Gaussian point source with width of 0.5*a* is placed 0.5*a* away from the PC, which has a dimension of . In Fig. 3(b), for a given incident wave along direction , and represent the corresponding refractive direction for TE mode and TM mode, respectively.

(Color online) The band structures of triangular-lattice air-holes PCs with different parameters. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively.

(Color online) The band structures of triangular-lattice air-holes PCs with different parameters. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively.

(Color online) The band structures of triangular-lattice APCs with different values of *r* _{2} when *n* _{0} = 1.52, *n* _{2} = 3.4, and *r* _{1} = 0.40*a*. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively.

(Color online) The band structures of triangular-lattice APCs with different values of *r* _{2} when *n* _{0} = 1.52, *n* _{2} = 3.4, and *r* _{1} = 0.40*a*. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively.

(Color online) (a) On condition that *n _{eff} * = −1, the common frequency

*ω*

_{com}, frequency difference Δ

*ω*, and radius

*r*

_{2}vs radius

*r*

_{1}in APCs when

*n*

_{0}= 1.52 and

*n*

_{2}= 3.4. The inset shows the enlarged view of scanned curve for Δ

*ω*. (b) Systematic comparisons of the quarter EFS for different values of

*r*

_{1}and

*r*

_{2}in APCs. The negative refraction effect is absent for TE mode when

*r*

_{1}is 0.42

*a*. Such “disturbance” behavior is in agreement with that found in Fig. 6(a).

(Color online) (a) On condition that *n _{eff} * = −1, the common frequency

*ω*

_{com}, frequency difference Δ

*ω*, and radius

*r*

_{2}vs radius

*r*

_{1}in APCs when

*n*

_{0}= 1.52 and

*n*

_{2}= 3.4. The inset shows the enlarged view of scanned curve for Δ

*ω*. (b) Systematic comparisons of the quarter EFS for different values of

*r*

_{1}and

*r*

_{2}in APCs. The negative refraction effect is absent for TE mode when

*r*

_{1}is 0.42

*a*. Such “disturbance” behavior is in agreement with that found in Fig. 6(a).

(Color online) The band structures of triangular-lattice APCs with different values of *r* _{1} and *r* _{2} when *n* _{0} = 1.52 and *n* _{2} = 3.4. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively. Point “C” corresponds to the edge of TE-2 band.

(Color online) The band structures of triangular-lattice APCs with different values of *r* _{1} and *r* _{2} when *n* _{0} = 1.52 and *n* _{2} = 3.4. Points “A” and “B” correspond to the peak of TE-2 band and TM-2 band, respectively. Point “C” corresponds to the edge of TE-2 band.

(Color online) The EFSs [(a)-(c)] and corresponding FDTD simulation of electric-field distribution [(d)-(f)] for APCs with different values of *r* _{1} and *r* _{2} when *n* _{0} = 1.52 and *n* _{2} = 3.4. In Fig. 8(a), for a given incident wave along direction , and represent the corresponding refractive direction for TE mode and TM mode, respectively. represents the maximum incident angle for negative refraction of TM mode, and it is about 32°, 37°, and 43° for Figs. 8(a)–8(c), respectively. (Right side of Fig. 8(f)): The cross-section distribution of normalized intensity for images in Fig. 8(f).

(Color online) The EFSs [(a)-(c)] and corresponding FDTD simulation of electric-field distribution [(d)-(f)] for APCs with different values of *r* _{1} and *r* _{2} when *n* _{0} = 1.52 and *n* _{2} = 3.4. In Fig. 8(a), for a given incident wave along direction , and represent the corresponding refractive direction for TE mode and TM mode, respectively. represents the maximum incident angle for negative refraction of TM mode, and it is about 32°, 37°, and 43° for Figs. 8(a)–8(c), respectively. (Right side of Fig. 8(f)): The cross-section distribution of normalized intensity for images in Fig. 8(f).

Article metrics loading...

Full text loading...

Commenting has been disabled for this content