Metamaterials for optical applications
Introduction |
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Since Abbe it’s well known that the resolution of a microscope is limited by diffraction. Due to this limitation conventional optical methods are hardly applicable for nanostructured surfaces that have become standard in semiconductor industry.
Therefore, it’s desirable to have a simple, non-destructive optical imaging system for creating high-resolution images in the visible domain and near infrared.
Crucial for the realization of such an optical system are the theoretical studies of V. G. Veselago [1] which proposed materials with a negative index of refraction for the first time in 1967. Using materials with a negative dielectric permittivity ε and a magnetic permeability µ the refractive index n becomes negative as well. Taking a closer look, this would result in a Poynting vector that is in the opposite direction of the wave vector and therefore the wave vector k, the magnetic field H and the electric field E yield a left-handed system (Fig. 1a).
The fields of application for metamaterials with a negative index of refraction are diverse. For our institute the optical properties of materials with a negative index of refraction are particularly interesting because they enable theoretically a perfect imaging lens [2] (Fig. 1b).
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Fig. 1: (a) Behavior of a TM wave in a material with a negative index of refraction. (b) J. B. Pendry’s superlens consisting of a material with n=-1 |
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Principle of operation |
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Because there are no existing materials with a negative refractive index in nature, they have to be designed and manufactured artificially. Periodical nanostructures with lattice periods well below the wavelength are one out of several options to tailor the electric and magnetic responses. For applications in the visible domain lateral sizes are in the range of 100nm.
Very promising structures are meander-type structures [3], which can act as resonators for optical wavelengths and, hence, be used to transfer evanescent near field modes to the far field. Additionally, to receive a magnified image of a sub-wavelength source, a geometrical structure has to be superimposed. Such a superstrate could be a convex surface similar to a conventional lens (Fig. 2a) or a slant surface [4]. Another option is the use of aperiodic meander structures utilizing enhanced optical transmission and resonant local field enhancement (Fig. 2b).
Optical elements that can resolve a wavelength below the diffraction limit are called “ superlenses” or “hyperlenses”, respectively. By the means of such a superlens a regular microscope can be used to non-destructively and without any processing resolve sub-wavelength structures.
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Fig. 2: Superstrates for the transformation from near to far field. (a) Convex surfaces comprised of alternating layers of dielectric and metal. (b) Resonant meander-type structure with different grating periodicities. Both structures are able to magnify sub-wavelength structures. Simulations have been done at ITO. |
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Goals |
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The key to understanding the underlying physical principles of the imaging properties of metamaterial structures is the simulation of resonant interactions between excited surface waves (surface plasmon polaritons) and the electromagnetic field. Particularly suitable are rigorous methods like RCWA (Rigorous Coupled Wave Algorithm) which is utilized in Microsim, a software that was developed at our institute.
Imaging and magnifying metamaterial structures at ITO are currently a topic of research, simulation, optimization and development. Furthermore, due to the complex calculation algorithms, convergence enhancements play a major role in terms of computation time reduction (especially for structures comprised of metal).
The performance of the manufactured structures is evaluated by means of optical measurements and the retrieved parameters will be used for further improvements of the simulation. The final goal is to build a “superlens” based on nanostructure-manufacturing processes.
Superlens results |
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It has been shown that surface plasmon polaritons (SPPs) propagating on the metal/dielectric interfaces of a bulk negative index material (NIM) have a dominant influence on the unique properties of these materials. Consequently, one could replace bulk NIMs by resonantly coupled surfaces that allow the propagation of SPPs [5].
A metallic meander structure (Fig. 3a) is perfectly suited as such a resonant surface due to the tunability of the short range SPP (SRSPP) and long range SPP (LRSPP) frequencies by means of geometrical variation [6].
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Fig. 3: (a) Principle design of a meander structure. (b) Two meander structures stacked onto each other mimic perfect imaging. |
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We demonstrated numerically how a stack consisting of two meander structures can mimic perfect imaging known from Pendry’s lens [7] (Fig. 3b). On the other hand, to observe sub-wavelength features in the far-field more than (perfect) near-field imaging is necessary. Therefore, we have investigated stacks of meander structures with successively increasing periodicity (Fig. 4a) capable to decrease the lateral wave vector until near-field to far-field transformation is achieved (Fig. 4b). This method has been shown to work numerically and the structure seen in Fig. 4a is in the process to be fabricated at our institute via focused ion beam (FIB) milling.
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Fig. 4: (a) Electric field intensity of a meander stack with different periodicities behind two slits in a Cr mask given in arbitrary units. (b) Magnification at λ = 500 nm. The slits are 250 nm apart and can be resolved with a regular microscope two wavelengths behind the meander stack (white dashed line in |
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Polarization scrambler results |
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Within a well-defined pass band, meander structures behave like almost ideal linear polarizers, can induce large phase retardation between s- and p-polarized light and show a high polarization conversion efficiency. In this respect, meander structures behave similar to plasmonic nanoslits at Fano resonance [8, 9] (Fig. 5) but over a wider frequency range and with a higher transmission. Due to these properties, meander structures can interact effectively with polarized light and can be used for different, non-imaging applications such as polarization scramblers [9, 10].
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Fig. 5: (a) Transmittance spectra of p-polarized (Tp) and s-polarized light (Ts) as a function of the azimuth angle ϕ at normal incidence for f = 600 THz, 630 THz and 650 THz. The fit curves are indicated by markers and were obtained from a model using plasmonic nanoslits at Fano resonance (b) Phase retardation δ as a function of the azimuth angle ϕ. (c) Transmittance of p-polarized light as a function of the azimuth angle ϕ for incident s-polarized light. The investigated meander structure has the geometry parameters Px = 400 nm, D = 40 nm and t = 30 nm. |
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The proposed polarization scrambler consists of spatially distributed metallic meander structures with random angular orientations. We describe the polarization properties of meander structures or meander stacks with the Mueller matrix (Fig. 6a). The whole device has an optical response averaged over all pixel orientations within the incident beam diameter. Averaging over all azimuth angles leads to a more intuitive representation of the depolarization properties of the proposed polarization scrambler (Fig. 6b).
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Fig. 6: (a) Mueller matrix (elements mij with row index i = 0-3 and column index j = 0-3) of a double meander structure at 600 THz with period Px = 400 nm, corrugation depth D = 40 nm and thickness t = 30 nm. The structures are stacked on top of each other separated by a layer of air with thickness Dspa = 600 nm. (b) Mueller matrix elements from (a) averaged over the azimuth angle ϕ from 0° to 180°. |
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One can see that for small angles all off-diagonal Mueller matrix elements are zero whereas the diagonal elements are reduced to values below one. In this angle regime, the device represents a partial depolarizer. With our preliminary design, we achieve depolarization rates larger than 50% for arbitrarily polarized monochromatic and narrow-band light. Circularly polarized light could be depolarized by up to 95% at 600 THz. The presented polarization scrambler can be flexibly designed to work at any wavelength in the visible and infrared range with a bandwidth of up to 100 THz. The proposed device might prove advantageous for optical setups with monochromatic light sources and is desirable for space applications due to its low weight and large-scale manufacturability
References |
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| [1] |
V.G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509 (1968). |
| [2] | J.B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966-3969 (2000). |
| [3] | L. Fu, H. Schweizer, T. Weiss, and H. Giessen, “Optical properties of metallic meanders,” J. Opt. Soc. Am. B 26, B111-B119 (2009). |
| [4] |
A. Salandrino, N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations,” Phys. Rev. B. 74, 075103 (2006). |
| [5] |
P. Alitalo, C. R. Simovski, A. Viitanen, and S. A. Tretyakov, “Near-field enhancement and subwavelength imaging in the optical region using a pair of two-dimensional arrays of metal nanospheres,” Phys. Rev. B 74, 235425 (2006). |
| [6] |
P. Schau, K. Frenner, L. Fu, H. Schweizer, and W. Osten, “Coupling between surface plasmons and Fabry-Pérot modes in metallic double meander structures,” Proc. SPIE 7711, 77111F (2010). |
| [7] | P. Schau, K. Frenner, L. Fu, H. Schweizer, H. Giessen, and W. Osten, ”Design of high-transmission metallic meander stacks with different grating periodicities for subwavelength-imaging applications,” Opt. Express 19(4), 3627-3636 (2011). |
| [8] |
M. Shcherbakov, M. Dobynde, T. Dolgova, D.-P. Tsai, and A. Fedyanin, “Full Poincaré sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82, 193402 (2010). |
| [9] | P. Schau, L. Fu, K. Frenner, M. Schäferling, H. Schweizer, H. Giessen, L. M. Gaspar Venancio, and W. Osten, “Polarization scramblers with plasmonic meander-type metamaterials”, Opt. Express 20(19) – to be published |
| [10] | P. Schau, L. Fu, K. Frenner, H. Schweizer, M. Schaferling, T. Weiss, H. Giessen, L. M. Gaspar Venancio, S. Hannemann, and W. Osten, “Polarization scrambling with metallic meander structures for space applications,” Proc. SPIE 8423, 842314, (2012). |