Mitrofanov, Oleg

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Oleg MitrofanovUCL1Winter College on Optics (ICTP)Terahertz Optics and Photonics Trieste, ItalyFeb 6-17, 2023 THz near-field Imaging and Spectroscopy:Fundamentals, Technology and Current Trendso.mitrofanov@ucl.ac.ukL. Hale et al., Laser. & Photon. Rev. 14 (4), 1900254 (2020) (illustration: T. Siday)THz ImagingHu and Nuss(1995)THz Imaging – Spatial ResolutionHu and Nuss(1995)THz Imaging – Subwavelength Spatial Resolution4Hu and Nuss(1995)THz Near-Field Microscopy Application Space5Wide range of subwavelength size systemsd / l10.10.011e-5    1e-4 1e-3300µm30µm3µm300nm30nmWaveguide modes, structured beamsPlasmons, metasurfaces, photonic crystals,  bio-tissueBiological cells, THz resonatorsnanowires, 2D materials Molecules, quantum dots, excitonsHow do we enable THz imaging?THz Near-Field Microscopy Application Space6Boland et al. THz Roadmap (2023)Graphics: Tom SidayTutorial Scope and Aims7THz near-field Microscopy Approaches THz near-field microscopy applications Right instrument for a given problemAppropriate problems for a given instrument? ? ? ?Tutorial Topics8Fundamentals of THz near-field microscopyExamples: Microscopy and Spectroscopy of THz resonatorsImaging of THz surface plasmon wavesImage interpretationTechnology: Subwavelength aperture and Scattering tip probesImproving sensitivity in THz microscopyCurrent Trends in THz microscopy methodsSpatial Resolution 9Ernst Abbe (c. 1873)Hu and Nuss(1995)Spatial Resolution 10Ernst Abbe (c. 1873)Far-Field – propagating waves: point-spread function limits resolving two pointsIntensityPosition, x/l10Spatial Resolution ~ l11Spatial Resolution 12~ lSpatial Resolution << l~ l13Spatial Resolution << l~ lEvanescent waves allow EM wave confinement on subwavelength scale)()0(),( tkziTT eEtzEw-=14Induced chargesandPolarization Angular spectrum representation of EM fields15How to include Evanescent Waves into analysis framework?Angular spectrum representation of EM fieldsyxkykxSpatial distribution16Angular spectrum representation of EM fieldsyxkykxSpatial distribution17[ ]dxdyeyxEkkE ykxkixyyxyx +-òò= ),(41),( 2p2D Fourier transform Angular spectrum representation of EM fieldsyxkykxSpatial distributionk-space distributionE(x,y) is a superposition of waves E(k) e ikr+ifFourier Transform18[ ]dxdyeyxEkkE ykxkixyyxyx +-òò= ),(41),( 2p2D Fourier transform Angular spectrum representation of EM fields19yxkykxSpatial distributionk-space distributionFourier Transform2D Fourier transform Angular spectrum representation of EM fields20yxkykxSpatial distributionk-space distributionFourier Transformkx2 + ky2 = k022D Fourier transform Angular spectrum representation of EM fieldsyxkykxSpatial distributionk-space distributionkx2 + ky2 + kz2 == k02Fourier Transform21Angular spectrum representation of EM fieldskx2 + ky2 + kz2 = k02kykxk0kz- imaginarykz- realAny subwavelength field distribution contains imaginary kz components – evanescent waves, localized near objects and interfaces kt < k0 = 2p / lkz2 > 0kt > k0 = 2p / lkz2 < 022Angular spectrum representation of EM fieldskx2 + ky2 + kz2 = k02kykxk0kz- imaginarykz- realAny subwavelength field distribution contains imaginary kz components – evanescent waves, localized near objects and interfaces kt < k0 = 2p / lkz2 > 0kt > k0 = 2p / lkz2 < 023Angular spectrum representation - Examples24yxkykxyxkykxk0k0THz Field Confinement25Opt. Express 20, 6197 (2012 )100 x 100µm  THz Field Confinement26Opt. Express 20, 6197 (2012 )100 x 100µm  l ~ 200 µmd < 10 µm THz Field Confinement27Opt. Express 20, 6197 (2012 )l ~ 200 µmd < 10 µm k0kxkykz- imaginary100 x 100µm  Representation  in k-space28k0kxkykxPropagating waves Evanescent waves –k0 k0E(kx)E(k)THz Field Confinement29100 x 100µmDz = 4 µm Dz = 8 µmDz = 0 µm Dz = 1.5 µmOpt. Express 20, 6197 (2012 )0 50 1000.00.51.0  Intensity (norm.)Dz (µm)0 1 2 3-101Etime (ps)100 x 100µm  l ~ 200 µmd < 10 µm kz2 > 0kz2 < 0d ~ 20 µm lMD ~ 300µmHigh permittivity Dielectric ResonatorTiO2 sphere:30d / l ~ 0.07Mie resonances in TiO2 spheresOptics Express, 22, 23034 (2014)M31e ~ 80-100d ~ 20 µm lMD ~ 300µmd / l ~ 0.07kt >>  k0Resonance Mode representation  in k-space32k0kxkyE(k)NF probing using subwavelength aperture33NF probing using subwavelength aperture34Optics Express, 22, 23034 (2014)No effect on transmission away from resonance Enhancement factor and width to quantify the resonatorInterference minimum (Fano line-shape)NF probing using subwavelength aperture20 GHz35MDEDOptics Express, 22, 23034 (2014)Subwavelength StructureNear-field structure in time-domainM1M2Resonator non-sphericity M1M2MyResonator non-sphericity Optics Express, 22, 23034 (2014)time (ps)in phase φ = 90°MD1MD21/(4Δf) ≈ 4 ps40Anisotropic Dielectric THz Resonators: I. Khromova et al., Laser and Photon. Reviews (2016)Near-field spectroscopy allows ‘seeing’ two modesSingle crystal TiO2:   ee = ~150; eo = ~70Spatial Resolution 41Ernst Abbe (c. 1873)Hu and Nuss(1995)20 µmSubwavelength resolution reveals additional structure in the fieldsCan near-field microscopy improve sensitivity?42What is far-field effect due to single resonator? Sub-wavelength sizeof TiO2 resonators Probing of single resonator – Scattering viewd ~ 20 µm lMD ~ 300µm43Sub-wavelength sizeof TiO2 resonators Probing of single resonator – Scattering viewTotal scattered power reduces due to the physical cross-section scaling with n -2Far-field total extinction by a single TiO2 sphere 0.1-1.0%(est. for typical THz-TDS) 1 3 5 7 9 11051015202530  Scattering efficiencyRefractive index, nwater dropletsSi spheresTiO2intrinsic absorptionMie Scatteringd ~ 20 µm lMD ~ 300µm44Sub-wavelength sizeof TiO2 resonators Probing of single resonator – Scattering viewd ~ 20 µm lMD ~ 300µmFar-field total extinction by a single TiO2 sphere 0.1-1.0%(est. for typical THz-TDS) Near-field:45ETH: J. Keller, G. Scalari, J. FaistSingle resonator sensitivity – Plasmonic resonator46ETH: J. Keller, G. Scalari, J. FaistSingle resonator sensitivity – Plasmonic resonator47L. Hale et al., Laser. & Photon. Rev. 14, 1900254 (2020)(illustration: T. Siday)ETH: J. Keller, G. Scalari, J. FaistSingle resonator sensitivity – Plasmonic resonator48Frequency (THz) Frequency (THz)0.5            1.0             1.5             2.0 0.5            1.0             1.5             2.0What is detected in THz NF microscopy?49What are the waves detected on metallic surface?L. Hale et al., Laser. & Photon. Rev. 14, 1900254 (2020) L. Hale et al., Laser. & Photon. Rev. 14, 1900254 (2020) 50Surface plasmon waves – THz-a-SNOML. Hale et al., Laser. & Photon. Rev. 14, 1900254 (2020) Tutorial Topics51Fundamentals of THz near-field microscopyExamples: Microscopy and Spectroscopy of THz resonatorsImaging of THz surface plasmon wavesImage interpretationTechnology: Subwavelength aperture and Scattering tip probesImproving sensitivity in THz microscopyCurrent Trends in THz microscopy methodsAcknowledgement52L. Hale, T. Siday (U. Regensburg), R. Hermans (Industry), A. Macfaden (U. Cambridge), R. Mueckstein (Industry), M. Navarro-Cia (U. Birmingham), M. Natrella (Industry), and R. ThompsonUniversity College LondonJ. Reno, I. Brener, T. Harris, T.S. Luk and W. PanCINT, Sandia National LaboratoriesL. Viti, M. C. Giordano, E. Dardanis, and M. S. VitielloCNR-Nano, ItalyW. Yu, C. Berger, W. A. de Heer, and Z. Jiang Georgia Tech. Y. Todorov, D. Gacemi, A. Mottaghizadeh and C. SirtoriUniv. Paris Diderot, Paris, FranceZ. Han, F. Ding and S. I. BozhevolnyiChina Jiliang University and DTU, DenmarkJ. Keller, G. Scalari and J. FaistETH-Zurich I. Khromova (U. Navarra) P. Mounaix (CNRS, Bordeaux), P. Kuzel (Czech Acad. Sci.)Results/Graphs from other groupsApplications in THz technology research: WaveguidesAPL. 94, 171104 (2009)THz waveguide10 µm aperture probeApplications in THz technology research: Waveguides10 µm aperture probeTHz Surface Plasmon Waves55Mitrofanov et al.J. STQE 103, 600 (2001)  SPP resonance on the bow-tie surfaceMueckstein et al., J.of IRMMW 32, 1031 (2011)Surface Waves on Gr Bow-Tie Antenna57-1             0.8            -0.6t1-1            0.75           -0.5time (ps)E (a.u.)E E 100 µmt1             t2t2Optical image (enhanced contrast)Metallic Bow-tie antenna Mueckstein et al., J.of IRMMW 32, 1031 (2011)Epitaxial monolayer graphene - Gr on C-face SiCOM et al. Solid State Comm. 224, 47-52 (2015) 

THz near-field imaging and spectroscopy: fundamentals, technology and current trends

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THz near-field imaging and spectroscopy: fundamentals, technology and current trends

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