Spectral negative refraction and focusing analysis of a two-dimensional left-handed photonic crystal lens

We report the spectral refraction analysis and focusing properties of a two-dimensional, dielectric photonic crystal (PC) slab in freespace. A transverse electric polarized upper band of the crystal is used. The measured refraction spectra indicates that a highly isotropic negative index of refraction is present in the measured frequency range of the band. We demonstrate experimentally and numerically the focusing of the field emitted from an omnidirectional source placed in front of the crystal. Both the source and the focus pattern are away from the PC interfaces of the order of several wavelengths. The focus pattern mimics the arbitrary lateral and longitudinal shifts of the source, which is a manifestation of true flat lens behavior.

Figure 1

(Color online) (top) TE polarized band structure of the PC. 5th band (shaded) gives negative refraction. (bottom) The surface (transparent shell) of the 5th band in the full Brillouin zone. Some equal frequency contours are projected to the Brillouin zone plane.

Figure 2

(Color online) Schematic of the refraction spectra measurement setup. The EM wave is emitted from a horn antenna, incident to the PC at ${\theta }_i$. The lateral intensity distribution of the refracted beam at the other interface is scanned by a monopole antenna. An HP8510C network analyzer is used to obtain the transmission spectra.

Figure 3

(Color online) (a) Measured negative refraction spectra of the 5th band along the PC-air interface for incidence angles $\theta =15°$, $30°$, and $45°$. Measured (b) and simulated (c) intensity profiles at $f=41.7\mathrm{GHz}$ for the respective incidence angles. Solid curves indicate Gaussian fits.

Figure 4

(Color online) Simulated negative refraction of a plane wave at $f=41.7\mathrm{GHz}$ incident at $\theta =30°$ to the PC interface (mark 1). Zero order (mark 2) and higher order (mark 3) reflections occur. The refracted (mark 4) the transmitted (mark 5) components appear to propagate as single beams.

Figure 5

(Color online) (a) Lateral intensity profiles measured at six different positions along the propagation direction: $z∕\lambda =1.78$, 3.56, 5.34, 7.12, 8.90, and 10.68. $z=0$ corresponds to the PC interface (b) Simulated 2D intensity in the image plane.

Figure 6

The measured (symbols) and simulated (solid curves) lateral intensity profiles at the focal distance $\left(z∕\lambda \approx 8\right)$ for different lateral shifts. The respective source locations are denoted by vertical dashed lines.

Figure 7

(Color online) Simulated 2D field distribution $H_y\left(x,z\right)$ for $d_{\mathrm{src}}=2\lambda$ (top) and $d_{\mathrm{src}}=4\lambda$ (bottom).

Figure 8

The measured lateral intensity profiles at respective focal distances for different source distances. The intensity axis is normalized by the $d_{\mathrm{src}}=2.0\lambda$ profile peak. The dashed line denotes the intensity profile in the absence of PC for $d_{\mathrm{src}}=2\lambda$.