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Metal-mesh technology: a past and present view Lorenzo Moncelsi presenting the work of many at Cardiff University: P. Ade, J. Zhang, P. Mauskopf, G. Savini (UCL), C. Tucker, G. Pisano (Manchester) 1. introduction Outline: 2. metal-mesh filters (single- and multi-grid) • theoretical elements • manufacture • performance and limitations 3. tunable artificial dielectric meta-material (Zhang et al. 2009) • theory and modelling • application as broadband anti-reflection coating – spectral measurements 4. achromatic metal-mesh half-wave plate (Zhang et al. 2011) • theory and modelling • measured spectral performance and comparison to crystalline HWPs 5. discussion and conclusions Ade et al. @ QMC and Cardiff University Development of quasi-optical components at FIR through (sub)mm wavelengths using metal-mesh technology. Deployed in many ground-, balloon-, and space-based instruments (from ISO to Herschel/Planck) Applications: Filters (LP, HP, BP, shaders) Dichroics Beam dividers Polarizers Wave-Plate retarders Anti-reflection coatings Lenses (?) Single Grids complementary THEORY (Ulrich 1967): • model as an oscillating circuit using transmission line formalism to explain the transmission properties • each grid/mesh is considered as one or more lumped circuit elements in a free-space transmission line • works well in the non-diffraction region (λ > g) and for normal incidence ASSUMPTIONS: • thin grids (t << a) • infinite conductivity • the supporting dielectric film has no effect, i.e. no absorption Single Grids - theory Ulrich 1967 plane wave (of unit amplitude) incident on grid define: - “normalized” frequency → ω = g / λ - reflection coefficient → Γ(ω) - transmission coefficient → τ(ω) 0th-order reflected/transmitted wave (lossless) and phases can be measured T and R waves are 90° out-of-phase Why are the inductive (capacitive) grids in the positive (negative) hemisphere ??? 2Y (ω ) − Y (ω ) Γ(ω ) = 1 + Y (ω ) voltage reflection coefficient admittance = 1/Z lossless grid − iX Y (ω ) = iB (ω ) = 2 X + R2 susceptance X (ω ) = ωL > 0 −1 X (ω ) = <0 ωC reactance Single Grids - theory Ulrich 1967 plane wave (of unit amplitude) incident on grid define: - “normalized” frequency → ω = g / λ - reflection coefficient → Γ(ω) - transmission coefficient → τ(ω) 0th-order reflected/transmitted wave (lossless) and phases can be measured T and R waves are 90° out-of-phase grids are complementary – Babinet’s principle L grid → continuous metal → DC currents reflect the entire incident wave for λ >> g high-pass filter low-pass filter Ulrich 1967 Characteristic lumped impedance and geometry of the grid characteristic impedance of a thin, lossless, grid only depends on the ratio a/g (“shape parameter”) of the dimensions of the grid. Marcuvitz 1951 derived for a 1D, thin, capacitive strip grating, i.e. electric vector of the incident wave is polarized ┴ to the lines of the grating. Also, normal incidence and λ >> g. • the 2D grid differs from the 1D grating only by the additional gaps of width 2a in the strips of the grating t/g=0.055 t/g=0.020 • as these gaps are oriented || to the electrical field and thus to the surface currents in the strips, their presence has only little influence on currents, and it completely vanishes as 2a→0 • the formula above works well for low a/g ratios (≤ 0.12) Ulrich 1967 Multi-grid interference filters (Ade et al. 2006; Tucker & Ade 2006) • in-band transmission close to 1 • steep slope at the frequency cut-off • strong out-of band rejection • stack several grids together with spacing between grids d = g/2ω0 = λ0/2, d where ω0(a/g) = 1 – 0.27 (a/g) and λ0 is the resonant wavelength • equivalent circuit = transmission line of uniform impedance, shunted by a number of lumped parallel or series resonant circuits which represent the grids • the model breaks down when spacing d << λ due to capacitive coupling between layers. For d > λ there is no interference → shallow cut-off slope • cut-off can be sharpened at the expense of ripples in the pass band • ripples can be reduced by mixing together meshes with differing characteristic impedances (geometries) • the edge slope increases with the number of elements (usually m = 6–12 grids) • random orientation of each layer maximizes the reflection of the unwanted high frequency radiation (prevents double diffraction) and minimizes polarizationdependent effects (Wood anomalies) Manufacture: air-gap vs hot-pressed filters • originally: inductive → electroformed free-standing wire meshes and capacitive → thermal evaporation onto a thin dielectric using the inductive grid as a mask • now: ultra-violet photolithography on dielectric layer to replicate the metal patterns over large areas with excellent control of the grid geometrical properties • both L and C grids: thin dielectric substrate of either Mylar (0.9–1.5μm) or polypropylene (≥3.3μm) coated with a thin (0.1–0.4μm) copper film • stack many single meshes together with plane parallel spacers to form the interference filter • spacers can be air-gaps or dielectric discs • air-gap devices need an annular support ring • dielectric spacers can be fused (hot-pressed) together with the mesh sheets to make a solid disc Ade et al. 2006 Performance: air-gap vs hot-pressed filters • air-gap: need annular ring support → less robust (not space qualified) • hot-pressed: very robust, easy to handle and cut to size → space qualified and well suited for cryogenic, large and compact focal plane systems • drawback: pass-band Fabry-Perot fringe due to the dielectric spacers when matched to free space. Polypropylene has little absorption but n = 1.48 • fringes can be tuned out by applying an anti-reflection coating air-gap hot-pressed • at high frequencies (≥ 30 cm-1) absorption from Mylar becomes significant and air-gap filters thus unsuitable Ade et al. 2006 Ade et al. 2006 Pisano et al. 2006 Non-idealities • absorption: ohmic (skin effect) and dielectric losses are non-zero. Increases with frequency but decreases with temperature P polarization • diffraction region: Floquet analysis, HFSS • C grids in non-normal incidence and fast optics: one C grid: 1st order diffraction ~ 20 cm-1 Woods anomaly, exact shape depends on polarization and grid orientation incidence angle 45° S polarization “ Shaders” 1 Np ≈ 8.7 dB Tucker & Ade 2006 • hot-pressed filter thickness t = (m+2) λ/4n, with m = # grids for a 10cm-1 LPE → m = 10 given nPP = 1.48 → t = 2mm • polypropylene absorption is maximum at 10μm (300K BB) • in large-aperture cryogenic systems, multi-grid filters would heat up in their central area (up to 240K for a 77K filter) and re-emit, causing severe IR loading onto the detectors • design of a thermal “shader” filter to strongly mitigate this effect: ultra thin substrate (low IR emissivity; can be warm) that reflects most of the incoming NIR power and has near-unit transmission in the FIR. Can stack several together as required. • SIMPLE: 3.3μm polypropylene substrate with capacitive grids on both sides “ Tucker & Ade 2006 Shaders” Artificial Dielectric Meta-material and its application as a mm and submm Anti-Reflection Coating Zhang et al. 2009 NOTE: used in the BLAST-Pol & PILOT HWPs attempted use on the EBEX HWP What the heck is a “meta-material” ??? • not Ron Artest’s new first name • “Meta-materials are artificial materials engineered to provide properties which may not be readily available in nature”. These materials usually gain their properties from structure rather than composition. • traditional metal-mesh components are not considered meta-materials because their electromagnetic properties are not independent of their thickness • closely spaced (but never d << λ) multiple layers of metal-mesh films embedded in polypropylene can behave as an artificial dielectric meta-material (ADM) Theory and modelling - Essential parameters in the build • Again, capacitive metal-mesh layers embedded in a base dielectric material (polypropylene) • Usual geometrical parameters in the model: 2a, g, d and m • bulk permittivity and permeability, corresponding to a material with effective index of refraction n • the effective permittivity of the artificial dielectric slab can be fine-tuned by varying a/g and d d m layers Zhang et al. 2009 Theory and modelling – HFSS simulations Use the High Frequency Structure Simulator (HFSS) to explore the optical properties of grid stacks with different geometries: Transmission as a function of frequency: • number of layers m = 10 • fixed grid ratio a/g = 0.28 • fixed g = 100μm • spacing d = 4 – 20μm Zhang et al. 2009 The refractive index n is derived from the transmission data by assuming that the resultant material behaves like a plane parallel dielectric Fabry-Perot intensity @ first minimum Tmin 4n 2 = 2 n +1 always μr≈1 perfect dielectric Theory and modelling – HFSS simulations Predicted refractive index n as a function of spacing d for: • m = 10, g = 100 μm • a/g = 0.05, 0.1, 0.28 • @ 5cm-1 (150GHz) • errors are 2% due to simulation accuracy. @150GHz Zhang et al. 2009 As a/g or d increase, the capacitance per unit length for an electric field || to grids decreases, and the effective permittivity of the material (and hence n) decreases a/g, d C/l εr , n Theory and modelling – HFSS simulations Predicted refractive index n as a function of frequency: • m = 10, g = 100 μm • fixed spacing d = 10μm • a/g = 0.05, 0.1, 0.28 • at fixed a/g, slight increase of n with frequency due to increase of g relative to the wavelength g/λ a/g n • n is independent of m, thus the material behaves as an artificial dielectric meta-material (ADM) over a wide range of wavelengths corresponding to g < λ Zhang et al. 2009 Theory and modelling HFSS model parameters for the anti-reflection coating (ARC) • ARCs are used to maximize a device’s transmission over spectral bandwidths approaching 100% 1. the material must have a range of appropriate n and high transparency over the required spectral band 2. the material must be mechanically suitable for bonding onto crystalline materials and for cryogenic temperatures • Previous ARC designs: 1. polypropylene layers loaded with high-n powders (TiO2) 2. ceramic-based materials (TMM) Savini et al. 2006 Theory and modelling HFSS model parameters for the anti-reflection coating (ARC) n = 2.1 Prototyped: ARC for a Z-cut crystal quartz plate: • two materials with intermediate refractive index close to 1.3 and 1.7 to achieve broad band tunable ADM m = 2, a/g = 0.14, g = 25.4μm d = 24μm, t = 40μm porous PTFE (Porex) t = 57μm ADM advantages: • complete control over n through geometry • control over thickness (PP has low absorption) • material is not brittle, easy to cut/handle Zhang et al. 2009 ADM drawback: CTE mismatch to crystals Spectral measurements measured ADM transmission vs simulation ADM alone target Zhang et al. 2009 Residual contour of the measured transmission vs the expected Fabry-Perot behavior of an ideal dielectric slab Spectral measurements quartz substrate AR- coated with ADM Discrepancies due to heat-bonding process in the press • porous PTFE: can be pressed to a smaller thickness • LDPE glue: can be absorbed by the PPTFE and slightly raise its n • PP: tends to relax and expand if there is not sufficient pressure on it Zhang et al. 2009 ADM - Conclusions • artificial dielectrics with refractive index above that of the base material can be obtained over a broad spectral band by fusing in layers of metal-mesh • the resultant refractive index can be easily controlled by adjusting the geometrical parameters of the meshes and the spacing between meshes • applied as a broadband anti-reflection coating for a Z-cut quartz substrate • successful cryogenic deployment on the BLAST-Pol and Pilot HWPs …less successful on the EBEX HWP (9 inch) due to CTE mismatch of PP (1%) vs sapphire (0.05%) Metal-mesh achromatic Half-Wave Plates for mm wavelengths Pisano et al. 2008 Zhang et al. 2011 “anisotropic” filter Shatrow (1995) C grids: - 2D array of metallic strips - looks capacitive to pol || strips - transparent to pol ┴ strips L grids: - narrow parallel conductors - looks inductive to pol || strips - transparent to pol ┴ strips Mesh HWP: 12-grid hot-pressed design @ 125–250 GHz Zhang et al. 2011 ADS model εPP = 2.19 - ADS is used for the transmission line modeling → return the optimized values of lumped inductances and capacitance - Criteria for the optimization of the impedances in ADS: • flat phase shift near 180° • maximize transmission in the frequency range 125–250 GHz Mesh HWP: 12-grid hot-pressed design @ 125–250 GHz Zhang et al. 2011 - HFSS is used to relate the geometric parameters of an individual mesh to its lumped impedance by breaking the physical mesh into cells and solving Maxwell’s equations on a cell-by-cell basis and thus obtaining the scattering matrices for radiation propagation through the mesh HFSS model - radiation with E || y-axis is transmitted through the L grids with a phase delay due to the optical path though the dielectric alone - similarly, the radiation with E || x-axis is transmitted through the C grids with a phase delay due to the optical path through the dielectric alone Mesh HWP: hot-pressed design L grids: - narrow parallel conductors - looks inductive to pol || strips - transparent to pol ┴ strips C grids: - periodic array of planar interdigital capacitor (IDC) coupled lines - achieves high effective lumped capacitance Zhang et al. 2011 C grids: - looks capacitive to pol || strips - transparent to pol ┴ strips Mesh HWP: hot-pressed device manufacture Zhang et al. 2011 - photolithography to produce the metal-mesh patterns in copper deposited onto thin substrates (8μm polypropylene) - additional non-metallized polypropylene layers create the appropriate spacing between grids; inductive and capacitive layers oriented orthogonally and then fused together - maintain good rotational and translational alignment between the layers Mesh HWP: hot-pressed results measured transmission Zhang et al. 2011 simulated 6-grid L/C phase shift copper thickness (0.1μm) ≈ skin depth at 1cm-1 measured x-pol measured phase shift Metal-mesh HWP - Conclusions • designed, built and fully characterized a prototype metal-mesh broadband achromatic HWP for mm wavelengths • the design can be scaled at higher frequency (submm) where crystalline absorption is indeed a problem • average transmissions for the two axes 86–91% and cross-pol ≤0.3% in-band • although the phase shift is not an improvement on existing crystalline devices, the HWP modulation efficiency is always ≥85% in a 90% spectral bandwidth • metal-mesh HWP advantages: - large maximum diameters (birefringent limited to ~300mm) - less expensive and heavy than crystals - space qualified - can be warm, in principle (low absorption) - unambiguous definition of “fast” and “slow” axis (for calibration; laser) References • Marcuvitz N., “Waveguide Handbook”, Mc.Graw-Hill, pp. 280-290 (1951) • Ulrich R., Infrared Physics, v. 7, pp. 37-50 (1967) • Ulrich R., Infrared Physics, v. 7, pp. 65-74 (1967) • Ulrich R., Applied Optics, v. 7, p. 1987 (1968) • Ulrich R., Applied Optics, v. 8, p. 319 (1969) • Shatrow A.D. et al., IEEE Trans. Antennas Propag., v. 43, pp. 109-113 (1995) • Ade P. et al., Proceedings of SPIE, v. 6275, p. 62750U (2006) • Tucker C. and Ade P., Proceedings of SPIE, v. 6275, p. 62750T (2006) • Pisano G. et al., Infrared Physics & Technology, v. 48, pp. 89-100 (2006) • Pisano G. et al., Applied Optics, v. 47, p. 6251 (2008) • Zhang, J. et al., Applied Optics, v. 48, p. 6635 (2009) • Zhang, J. et al., Applied Optics, v. 50, p. 3750 (2011)