Negative Refraction and Imaging Using 12-fold-Symmetry Quasicrystals

Abstract

Recently, negative refraction of electromagnetic waves in photonic crystals was demonstrated experimentally and subwavelength images were observed. However, these investigations all focused on the periodic structure. Here, we report a new theoretical and experimental finding that negative refraction can appear in some transparent quasicrystalline photonic structures. The photonic quasicrystals (PQCs) exhibit an effective refractive index close to ÿ1 in a certain frequency window. The index shows small spatial dispersion, consistent with the nearly homogeneous geometry of the quasicrystal. More interestingly, a superlens based on the 2D PQCs can form a non-near-field subwavelength image whose position varies with the source distance. These properties make PQCs promising for application in a range of optical devices.

Conical Dispersion and Effective Zero Refractive Index in Photonic Quasicrystals

“…Nonetheless, PQC can still have relatively sharp diffraction patterns due to longrange order. Such patterns confirm the existence of wave scattering and interference, providing similar functionalities as periodic counterparts, such as photonic band gaps [12][13][14][15], negative refraction [16], lasing [17][18][19], and nonlinear light propagations [20][21][22]. We will show theoretically and experimentally that some two-dimensional photonic quasicrystalline approximants can possess conical dispersion at k ¼ 0, and their finite-sized counterparts can behave like a zero-refractive-index medium as evidenced by different experimental measurements.…”

“…Photonic quasicrystal (PQC) is constructed by building blocks positioned on well-designed patterns but lacks translational symmetry [12][13][14][15][16][17][18][19][20][21][22][23]. Nonetheless, PQC can still have relatively sharp diffraction patterns due to longrange order.…”

“…Even amorphous photonic crystals support band gaps [32], but disorder as a precursor to level repulsion can eliminate the conical dispersion (Supplemental Material [25], Appendix G). This is unlike using quasicrystals to realize the effective negative index in which the negative index will persist independent of the detailed arrangement of the "atoms" as long as the filling ratio is correct [16]. In addition, one can also extend the concepts to optical frequencies as the PQC is constructed by all-dielectric and low-loss rods.…”

Negative Refraction by Photonic Crystal

“…The super-prism effect is another exciting property arising from the photonic crystals [19,32]. Extensive numerical [21,33,34] and experimental studies [35][36][37] provided a better understanding of negative refraction, focusing and sub-wavelength imaging in photonic crystal structures. Masaya Notomi showed that refraction-like behaviour could be expected to occur in photonic crystals that exhibit negative refraction for certain lattice parameters.…”

All-Angle Broadband Negative Refraction of Metal Waveguide Arrays in the Visible Range: Theoretical Analysis and Numerical Demonstration

“…It has been demonstrated theoretically and experimentally that both left-handed metamaterials [4 -7] and photonic crystals [8][9][10][11][12][13][14][15] can achieve NR from microwave to near-infrared frequencies. Furthermore, all-angle NR (AANR) for lens imaging at microwave frequencies by metamaterials [16,17] and at optical frequencies by photonic crystals [18,19] has also been demonstrated recently, but the operating bandwidth is still limited in a narrower frequency range [16 -19], and the realization of broadband AANR at an optical frequency, especially in the visible region, is still a challenge.Generally speaking, a periodic structure is capable of producing NR for electromagnetic waves. For example, a simple dielectric waveguide array can bend light in the direction opposite to that observed in common media at a limited incident angle within a narrow frequency bandwidth [20,21].…”