Metal-mesh technology: a past and present view

Lorenzo Moncelsipresenting the work of many at Cardiff University:P. Ade, J. Zhang, P. Mauskopf, G. Savini

(UCL),

C. Tucker, G. Pisano (Manchester)

1.

introduction

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

Outline:

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)DichroicsBeam dividersPolarizersWave-Plate retardersAnti-reflection coatingsLenses (?)

Ade et al. @ QMC and Cardiff University

ASSUMPTIONS:

• thin grids (t

<< a)

• infinite conductivity

•

the supporting dielectric film has no effect, i.e. no absorption

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

complementary

Single Grids

plane wave (of unit amplitude) incident on grid

define:- “normalized”

frequency → ω =

g

/ λ- reflection coefficient → Γ(ω)- transmission coefficient → τ(ω)

Ulrich 1967Single Grids -

theory

(lossless)

and phases can be measured

0th-order reflected/transmitted wave

)(1)()(ωωωYY+−

=Γ 22)()(RXiXiBY+

−== ωω

01)(

0)(

<−

=

>=

CX

LX

ωω

ωω

Why are the inductive (capacitive) grids in the positive (negative) hemisphere ???

T and R waves are 90°

out-of-phase

reactancesusceptanceadmittance = 1/Z

)(2 ωY

voltage reflectioncoefficient

lossless grid

plane wave (of unit amplitude) incident on grid

define:- “normalized”

frequency → ω =

g

/ λ- reflection coefficient → Γ(ω)- transmission coefficient → τ(ω)

Ulrich 1967

L

grid → continuous metal → DC currents reflect the entire incident wave for λ

>> g

high-pass filter

low-pass filter

Single Grids -

theory

(lossless)

and phases can be measured

grids are complementary –

Babinet’s

principle

0th-order reflected/transmitted wave

T and R waves are 90°

out-of-phase

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

•

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

t/g=0.055t/g=0.020

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, where ω0

(a/g) = 1 –

0.27 (a/g) and λ0

is the resonant wavelength d

•

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 polarization-

dependent 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)

•

at high frequencies (≥

30 cm-1) absorption from Mylar becomes significant and air-gap filters thus unsuitable

Ade et al. 2006

air-gaphot-pressed

•

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

•

absorption: ohmic

(skin effect) and dielectric losses are non-zero. Increases with frequency but decreases with temperature

•

diffraction region: Floquet

analysis, HFSS

•

C grids in non-normal incidence

and fast optics:

Woods anomaly, exact shape depends on polarization and grid orientation

Non-idealities Ade et al. 2006Pisano et al. 2006

one C

grid: 1st

order diffraction ~ 20 cm-1

P polarization

S polarization

incidence angle 45°

“Shaders”

• 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

Tucker & Ade 20061 Np

≈

8.7 dB

•

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

“Shaders”

Tucker & Ade 2006

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

HWPsattempted use on the EBEX

HWP

• 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)

What the heck is a “meta-material”

???

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

m layers

d

Zhang et al. 2009

Theory and modelling –

HFSS simulations

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

The refractive index n

is derived from the transmission data by assuming that the resultant material behaves like a plane parallel dielectric

142

2

min +=nnT

Fabry-Perot intensity@ first minimum

always μr

≈1perfect dielectric

Use the High Frequency Structure Simulator (HFSS) to explore the

optical properties of grid stacks with different geometries:

Zhang et al. 2009

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.

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

@150GHz

Zhang et al. 2009

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

Theory and modelling –

HFSS simulations

•

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

•

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

Theory and modellingHFSS model parameters for the anti-reflection coating (ARC)

•

Previous ARC designs:

1.

polypropylene layers loaded with high-n

powders (TiO2

)

2.

ceramic-based materials (TMM)

Savini

et al. 2006

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

Theory and modellingHFSS model parameters for the anti-reflection coating (ARC)

n

= 2.1

tunable

ADMm = 2, a/g

= 0.14, g

= 25.4μmd

= 24μm, t

= 40μmporous 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

ADM drawback: CTE mismatch to crystalsZhang et al. 2009

Spectral measurementsmeasured ADM transmission vs

simulation

Residual contour of the measured transmission vs

the expected Fabry-Perot behavior

of an ideal dielectric slab

target

ADM alone

Zhang et al. 2009

quartz substrate AR-

coated with ADM

Spectral measurements

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. 2008Zhang et al. 2011

“anisotropic”

filterShatrow

(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

-

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

-

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

Mesh HWP: hot-pressed design Zhang et al. 2011

C grids:-

looks capacitive to pol

|| strips- transparent to pol

┴

strips

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

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 Zhang et al. 2011

measured transmission

measured x-polmeasured phase shift

simulated 6-grid L/C phase shift

copper thickness (0.1μm) ≈

skin depth at 1cm-1

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)