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Transcript
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)