Abstract

We studied the optical properties of a dielectric photonic crystal structure with spirals arranged in a hexagonal lattice. The dielectric constant of the material was 9 and the filling ratio was 15.2%. We found that this kind of structure exhibits a significant polarization gap in the light that was incident along the axis of the spirals. The eigenmodes inside the polarization gap were predominantly right-hand (left-hand) polarized depending on the whether if the spirals are left-handed (right-handed). We calculated the transmission spectrum of a slab of such a structure and it matches well with the analysis of the eigenmodes.

© 2005 Optical Society of America

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References

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Abstract in PECS-VI (1)

O. M. Roche, D. N. Sharp, E. R. Dedman, A. J. Turberfield, C. F. Blanford, and R. G. Denning, �??Optically active photonic crystals by holographic lithography,�?? Abstract in PECS-VI, (2005).

Adv. Mater. (2)

P. W. Wei, W. Cheng, I. B. Martini, B. Dunn, B. J. Schwartz, and E. Yablonovitch, �??Two-photon photographic production of three-dimensional metallic structures within a dielectric matrix,�?? Adv. Mater. 12, 1438-1441, (2000).
[CrossRef]

I. Hodgkinson, and Q. H. Wu, �??Inorganic Chiral Optical Materials,�?? Adv. Mater. 13, 889-897, (2001).
[CrossRef]

Journal of Modern Optics (1)

J. B. Pendry, �??Photonic band structures,�?? Journal of Modern Optics 41 No. 2, 209-229, (1994).
[CrossRef]

Nano letters (1)

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, �??Fabrication of tetragonal square spiral photonic crystals,�?? Nano letters 2, 59-62, (2002).
[CrossRef]

Nature (1)

K. Robbie, D. J. Broer, and M. J. Brett, �??Chiral nematic order in liquid crystals imposed by an engineered inorganic nanostructure,�?? Nature 399, 764-766, (1999).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phy. Chem. (1)

See, e.g., I. Tinoco, Jr., M. P. Freeman, �??The optical activity of oriented copper helices. I. Experimental,�?? J. Phy. Chem. 61, 1196-1200, (1957).
[CrossRef]

Phys. Rev. B (1)

A. Chutinan, and S. Noda, �??Spiral three-dimensional photonic-band-gap structure,�?? Phys. Rev. B 57, 2006-2008, (1998).
[CrossRef]

Phys. Rev. E (1)

Z. Y. Li, and L. L. Lin, �??Photonic band structure solved by a plane-wave-based transfer-matrix method,�?? Phys. Rev. E 67, 046607, (2003).
[CrossRef]

Phys. Rev. Lett. (1)

C. Oldano, �??Existence of a critical tilt angle for the optical properties of chiral smectic liquid crystal,�?? Phys. Rev. Lett. 53, 2413-2416, (1984).
[CrossRef]

Science (3)

V.I. Kopp, V.M. Churikov, J. Singer, N. Chao, D. Neugroschl,1 A.Z. Genack, �??Chiral Fiber Gratings,�?? Science, 305, 74-75 (2004
[CrossRef] [PubMed]

O. Toader, and S. John, �??Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,�?? Science 292, 1133-1135, (2002).
[CrossRef]

J. B. Pendry, �??A chiral route to negative refractive,�?? Science 306, 1353-1355, (2004).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Transmission spectra for a 16-layer slab of the dielectric structure proposed by Toader [3] for (a) LH and (b) RH circularly polarized incident plane waves.

Fig. 2.
Fig. 2.

A schematic diagram of the spiral structure and its Brillouin points. (a) is the side view, (b) is the top view of the array and (c) gives the Brillouin points. The ΓA direction is along the z-axis. The spiral has a dielectric constant of ε= 9. The filling ratio of the structure is 15.2 %.

Fig. 3.
Fig. 3.

Transmission spectra and the band structure of the RH spiral structure shown in Fig 2. The incident plane wave is LH and RH circularly polarized in (a) and (b), respectively. The band structure is shown in (c). The transmission spectrum is calculated for 16 layers in the z-direction and the shaded areas mark polarization gaps. In (d), thin plates of a dielectric material are added in each period in the z-direction. Bands “a” and “b”, of different polarizations, are marked by red and blue colors, respectively.

Fig. 4.
Fig. 4.

Band structure along ΓA plotted in the extended zone scheme with the magnitude of the plane-wave components indicated by the sizes of the symbols. Panel (a) is for the structure with continuous spirals and (b) is for the structure with thin plates inserted in each period. Bragg scattering is barely observable in (a). The first Brillouin zone is the region bounded between ±0.5 (in units of kπ/a). Bands “a” and “b” are marked by circles and crosses, respectively.

Fig. 5.
Fig. 5.

The ratio between different components of the H-field in the (right-handed) spiral structure of Fig. 2. The ratio is expected to be 1 (-1) for right- (left-) handed circularly polarized waves.

Fig. 6.
Fig. 6.

Upper bounds (open circles) and lower bounds (crosses) of the coupling coefficient ratios of a circular-polarized plane-wave with eigenmodes of spiral structures. Panels (a) and (b) show the coupling coefficients for a RH and LH dielectric spiral, respectively.

Fig. 7.
Fig. 7.

The polarization gap as a function of k//. The region between the two curves is the frequency range in which only a single polarization is allowed inside the spiral structure. The dashed lines represent k// =ω/c.

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