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Vapor-deposited thin films with negative real refractive index in the visible regime J. J. Yi, A. Lakhatakia, W. Y. Ching, T.L. Chin Optics Express Vol 17, No 10 May 11 2009

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Introduction Metamaterials –artificial composite materials that, by their microstructure, exhibit properties not exhibited by their component materials

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Introduction Negatively refracting metamaterials –Consists of coupled, metallic, subwavelength elements that simulate electric and magnetic dipoles.

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Introduction In such metamaterial, an EM wave propagates so that the direction of its energy flow is opposed to its phase velocity, a condition captured by the real part of the refractive index being negative

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Introduction Negative refractive index can be made available by the fabrication of thin films using Oblique angle deposition techniques. These films are optically anisotropic, like biaxial crystal.

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OAD (e-beam) Silver Electron gun Substrate θ

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Theory In general, the equivalent relative permittivity tensor ε and the equivalent relative permeability tensor μ must have the same set of three eigenvalues. When the film is illuminated normally, different combinations of the eigenvalues of these tensors appear for the two polarization states (p- and s- polarized)

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Theory Refractive index Relative Intrinsic Impedance where v=p,s depending on the polarization

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Theory Both the n v and η v can be determined by measuring the reflection coefficient r v and the transmission coefficient τ v of the film of thickness d..

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Methodologyy 2-inch square substrates of fused silica (glass) Electron beam deposition Base pressure: 4x10 -6 Pa Deposition Rate: 0.3 nm/s Deposition angle: 86°86°

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Methodology The reflection and transmission coefficients were measured at specific λ’s using an ellipsometer and a walk-off interferometer.

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Methodology Diode lasers of λ=532 nm, 639 nm and 690 nm were used as light sources and the ellipsometer used was a PSA (Polarizer-Sample- Analyzer) system This yields the ration τ p /τ s

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Methodology The walk-off interferometer was used to measure τ s and both reflection coefficients “the incident laser beam is separated into two beams––one s- polarized and the other p- polarized.”

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Methodology “One of the polarized beams is normally incident on the sample (silver thin film) and the other polarized beam is incident on the bare substrate; the two reflected and transmitted beams combine and produce interference.”

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Methodology “The polarization state of the combined beam yields the absolute phase of the reflection coefficient or the transmission coefficient associated with a specific polarization state.”

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Resultss Film thickness: 240 nm Nanorods angle: 66°±5° Average nanorod length: 650 nm Average nanorod diameter: 80 nm

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Results

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s

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Discussion S-polarized –The real parts of ε, μ and n are all positive at all three wavelengths P-polarized –The real part of μ > 0 while the real part of ε < 0 at all three wavelengths. –Both the real and the imaginary part of ε increase with wavelength. Similar to that predicted by the plasmonic-type permittivity model for composites containing thin-wire metal inclusions

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Discussion P-polarized –The imaginary part of n > 0, while the real part of n < 0 at all three wavelengths. –-n p ’/n p ” lies between 0.3 and 0.65 over the 532-690 nm λnp’np’ 532 nm-0.705 639 nm-0.476 690 nm-0.552

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Conclusion A well-established thin-film technique, Oblique Angle Deposition, can be used to deposit thin films that refract light negatively. OAD is stable for depositing multilayered stacks used in optical filters and mirrors. Layers of a gain medium can be incorporated to offset any attenuation using

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