Фізика метаматеріалів та наноплазмоніки

🔬 Negative refractive index

Veselago prediction

n = -√(εr·μr) для negative εr, μr. Snell's law: negative refraction. Backward waves, reversed Doppler.

First demonstration

Smith (2000): SRR + wires. 10 GHz frequency. n ≈ -2.7. Left-handed materials (LHM).

Band structure

Bandgap, slow-light regime. Negative group velocity: vg < 0. Anomalous dispersion.

Applications

Lensing, cloaking, antennas. Superlens: perfect imaging. Subwavelength resolution.

🔬 Perfect lensing

Pendry lens

Negative index slab для subwavelength focusing. Evanescent waves amplification. Resolution < λ/2.

Surface plasmons

SPP resonance: evanescent coupling. Field enhancement ~10³-10⁶. Super-resolution.

Hyperlens

Cylindrical anisotropic media: magnification subwavelength features. λ ~ 400 nm → microscope resolution.

Super-resolution microscopy

STORM, PALM, STED. Metamaterial-enhanced: resolution < 10 нм. Optical nanoscopy.

🎭 Cloaking

Transformation optics

Coordinate mapping: cloaked region → free space. Maxwell's equations covariance. Material parameters.

Spherical cloak

Cylindrical → spherical transformation. Anisotropic ε, μ. R1 < r < R2. Ray bending.

THz cloaking

SRR-based: cloaks для THz. Experimental: 3-4 THz. Invisible для radar.

Broadband cloaks

Non-resonant approaches. Active cloaking. Losses: absorption, reflection. Practical challenges.

💎 Plasmonics

Surface plasmons

SPPs: ω² = c²k²(ε_m ε_d)/(ε_m + ε_d). Dispersion у metal-dielectric. Propagation length ~100 μm.

Localized SPPs

Nanoparticles (Au, Ag): localized modes. Mie scattering. LSPR: ~400-800 nm for Au spheres.

Field enhancement

E-field enhancement ~10³-10⁶. Hot spots. SERS: surface-enhanced Raman. Single-molecule detection.

Applications

SERS, biosensing, photovoltaics, data storage. Plasmonic circuits. Photonic chips.

🔬 Metamaterial design

Split-ring resonators

SRRs: magnetic response μ(ω). LC resonance: ω_LC ≈ 1/√(LC). Negative μ frequency bands.

Metal wires

Thin wires: Drude ε(ω). Plasma frequency ωp. Negative ε для ω < ωp.

Fishnet structures

Stacked metal-dielectric layers. Negative index broadband. NIM: negative index materials.

Effective medium

Homogenization: subwavelength structures → effective ε, μ. Maxwell Garnett, Bruggeman models.

🔬 Frequency regimes

Microwave

10 GHz: first demonstrations. SRRs + wires. Large structures, low losses. Antennas.

THz

0.3-30 THz: sensing gap. Plasmonic metamaterials. Cloaks, modulators.

Optical

Visible: fabricating challenges. Metal losses. Hyperbolic metamaterials. Super-resolution.

Losses

Metal absorption: Drude damping γ. Quality factor Q. Loss mitigation: gain, new materials.

📊 Графіки та діаграми

Drude model

ε(ω) для metals:

Negative ε: real part Re(ε) < 0. Metal dielectric function. Plasmon resonance.

SPP dispersion

Surface plasmon:

Light line ω/c: SPP above. Subwavelength confinement.

ε(ω) = 1 - ωp²/(ω(ω + iγ)) Де ωp ≈ 10¹⁶ рад/с (plasma frequency) γ ~ 10¹⁴ рад/с (damping) ε < 0 для ω < ωp

🧪 Практичні приклади

Приклад 1: First negative index

Smith (2000): SRR + wires. 10 GHz, n ≈ -2.7. Verification: refraction, phase velocity.

Приклад 2: THz cloak

SRR-based cloak: 3-4 THz. Cylindrical geometry. Ray bending, invisibility.

Приклад 3: SERS enhancement

Au nanoparticles: E-field ~10⁶. Single-molecule Raman. Plasmon hot spots.

Приклад 4: Hyperlens

Anisotropic cylindrical: λ → visible. Subwavelength magnification. Optical nanoscopy.

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Метаматеріали: штучна матеріальність

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