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Metamaterial Beats Natural Crystals in Spectral Filters

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Metamaterial Beats Natural Crystals in Spectral Filters Metamaterial beats natural crystals in spectral ¯lters: isolated transmission line at any prescribed wavelength N. I. Zheludev,1, ¤ E. Plum,1 and V. A. Fedotov1 1Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, SO17 1BJ, UK (Dated: June 1, 2011) PACS numbers: Spectral ¯lters are key components of telecom- transmit light. Torsional stress, magnetic ¯eld or natural munication, imaging, sensor and spectroscopic optical activity (circular birefringence) of the crystal it- devices. Optical ¯lters are achieved though engi- self could mix up the orthogonal polarization eigenstates neering of interferences in a complex multilayered and thus could act as the perturbation [1{4]. For in- structure, or by exploiting dispersion of absorp- stance, if natural optical activity rotates the polarization tion or anisotropy in natural media. In the mi- state of light a high background and ripples-free trans- crowave and terahertz regions frequency selective mission line centered at the isoindex point will be ob- surfaces are used to provide spectral selectivity. served, Fig. 1(a). The ¯lter's transmission line width 4¸ While being extremely good in some of their char- depends on the dispersion of birefringence @n=@¸ at the acteristics, narrow-band interference ¯lters su®er isoindex point: 4¸ = (¸0=2L)=(@n=@¸), while the opti- from a small acceptance angle, ¯lters based on mal length of the crystal L is governed by the condition absorption or anisotropy depend on the availabil- that circular birefringence (optical activity) rotates the ity of natural media to provide functionality at polarization state of light by GL = 90±. Here G is the the required wavelength and frequency selective speci¯c rotary power of the crystal at the isoindex point. surfaces often show multiple and wide transmis- To achieve a good quality ¯lter the birefringence shall sion bands. Here we demonstrate that a narrow- increase rapidly from the isoindex point, while optical band spectral ¯lter with a ripples-free isolated activity shall have a non-zero value. transmission peak and wide acceptance angle can Isoindex ¯lters have been extensively studied and be constructed exploiting polarization properties demonstrated with di®erent crystalline media [1{11], of a metal ¯lm patterned on the subwavelength most notable with CdS under torsion stress and CuAlSe2 scale. Its transmission band can be engineered to exploiting its natural optical activity. In crystal-based be anywhere from the visible to microwaves. isoindex ¯lters the transmission wavelength is prescribed We design our spectral ¯lter taking inspiration from by the crystal itself, for instance in CdS it is at ¸0 = polarization optical ¯lters which are widely know in op- 523 nm, while in CuAlSe2 it is at ¸0 = 531 nm. How- tics. One of the most elegant polarization ¯lters exhibit- ever, only a few isoindex crystals have been identi¯ed so ing a single isolated transmission line at a spectral posi- far. Thus wavelengths at which isoindex crystals can be tion that is independent of the light's incidence angle on constructed are sparse and little is know about crystals the ¯lter was suggested by Henry [1]. Its functionality de- with isoindex points in the infrared and beyond. Fur- pends on the energy exchange between two orthogonally thermore, isoindex crystals, which are often exotic com- polarized modes in a birefringent crystal in the proximity pounds, are extremely expensive, which hampers their of the spectral point ¸0 where birefringence @n = no ¡ne applications and technological proliferation. changes its sign, see Fig. 1(a). At this wavelength, known Here we show that the key element of the ¯lter, the as the \isoindex wavelength" birefringence vanishes and isoindex crystal, can be replaced by a metamaterial, an the crystal becomes isotropic. At wavelengths away from arti¯cial electromagnetic medium consisting of a regular the isoindex point, where birefringence is substantial, two array of sub-wavelength resonators, which can be engi- orthogonally polarized waves, the \ordinary" wave with neered to o®er a narrow-band spectral ¯lter at a pre- refractive index no and \extraordinary" wave with ne, scribed wavelength anywhere from the microwave to the are good eigenstates of the crystal and energy exchange visible part of the spectrum. Moreover we demonstrate between them does not take place. If the crystal is placed that it is su±cient to use a single layer, planar metama- between two crossed linear polarizers aligned along these terial structure to achieve the ¯lter. eigenpolarizations no light will be transmitted through Indeed, in planar metamaterials birefringence can be the device. easily derived from an asymmetry of the meta-molecule However, near the isoindex point a small perturbation while the interplay between di®erent modes of meta- can disturb the eigenstates and light passing through the molecular excitation can create a response with vanish- crystal changes its polarization state: at this wavelength ing birefringence at certain isoindex wavelengths. This the crystal sandwiched between crossed polarizers will is routinely observed with metamaterials in all parts of 2 a b optical activity is allowed by a chiral arrangement of the Isoindex incident wave vector and the low-symmetry metamaterial P2 α P2 gyrotropic Meta- pattern [15]. crystal material We have identi¯ed a class of birefringent planar meta- materials that show optical activity at the isoindex point. These metamaterials are arrays of asymmetrically split ring slits in a metal ¯lm. We have been able to demon- strate that when such a metamaterial structure is placed between a pair of crossed polarizers at some angle to the optical axis of the system (see Fig. 1(b)), a narrow-band, P P 1 1 ripples-free spectral ¯lter is formed. Such ¯lters, that we call metamaterial isoindex ¯lters (MIFs), have been Isoindex Isoindex manufactured and studied for the microwave and optical point point parts of the spectrum. 0 0 The microwave version of the metamaterial was an ar- ray of asymmetrically-split ring apertures with a unit cell of 15 £ 15 mm2. It was milled in a self-standing 1 mm Lin. birefringence λ λ Lin. birefringence λ λ 0 0 thick aluminum sheet (inset to Fig. 3(a)). Each split- ring aperture had a radius of 6 mm and consisted of 140± and 160± arc slits of 1 mm width. The photonic ver- sion of the metamaterial (inset to Fig. 3(b)) was based on a rectangular-shaped split-ring pattern. The slits of Opt. activity 0 Opt. activity 0 λ λ0 λ the pattern had the width of 50 nm and were etched in a 30 nm thick gold ¯lm on a 500 ¹m thick fused silica substrate using electron beam lithography. Five meta- material samples with respective unit cell sizes of 400, 425, 450, 475 and 500 nm were manufactured. The mi- crowave ¯lter was characterized in an anechoic chamber Transmission using linearly polarized antennas and a vector network 0 λ0 λ analyzer while the performance of the optical ¯lters was measured with a microspectrophotometer using dichroic FIG. 1: Isoindex gyrotropic spectral ¯lters. (a) In con- linear polarizers. ventional ¯lters of this type, a uniaxial optically active bire- At normal incidence the split-ring pattern allows two fringent crystal with accidental birefringence zero-crossing ¸ 0 orthogonal linearly polarized eigenstates oriented parallel is sandwiched between two orthogonal linear polarizers P and 1 and perpendicular to the splits. Although the pattern is P2. The crystal birefringence must change sign at wavelength ¸0, while optical activity (circular birefringence) should re- inherently anisotropic, there is a spectral point where main non-zero. (b) In metamaterial-based isoindex spectral linear birefringence and dichroism simultaneously vanish ¯lters, planar metamaterial tilted with respect to the ¯lter's giving rise to the isoindex point, see Fig. 2. Our analysis optical axis replaces the crystal. The metamaterial exhibits a shows that at this wavelength the anisotropy, native to birefringence zero-crossing isoindex point ¸0 on a background this metamaterial where the meta-molecules lack rotation of strong resonant optical activity. symmetry, is canceled through the interference of two modes associated with the short and long sections of the ring. the spectrum [12]. Perturbations that mix up the eigen- Optical activity of the structure is derived from anti- modes are less trivial to achieve. Natural optical activ- symmetric currents on either side of the slits, which give ity is a prime choice here as it does not require appli- rise to an overall magnetic dipole moment oscillating nor- cation of torsional stress or magnetic ¯eld. Metamateri- mal to the plane of the split rings [16]. At oblique in- als with strong optical activity are well known and they cidence the magnetic dipole has a component orthogo- are normally constructed from volume, thee-dimensional nal to the wave propagation direction and parallel to the meta-molecules [13, 14]. However, metamaterials with polarization of the incident wave [15]. As a result, our three-dimensional meta-molecules are di±cult to manu- planar metamaterial exhibits optical activity at the res- facture, in particular for the optical part of the spectrum. onance and the structure's two orthogonal linearly po- Fortunately, an elegant solution exists where optical ac- larized eigenstates become coupled, exactly in the same tivity can manifest itself in planar metamaterials. This way as in the crystal-based isoindex ¯lter, see Fig. 2(e- can take place
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