Effect of Mirror Defect and DamageOn Beam Quality

T.K. Mau and Mark TillackUniversity of California, San Diego

ARIES Project Meeting

March 8-9, 2001Livermore, California

OUTLINE

• Objectives of final optics study

• GIMM surface defect types and analysis approaches

• Summary of Fresnel modeling of gross surface contaminant on mirror performance

• Analytic estimate for microscopic surface damage

• Future plans

Geometry of the final laser optics

Prometheus-L reactor building layout

(30 m)

(SOMBRERO values in red)

(20 m)

• Goal of study is to determine design windows for GIMM and other optical subsystems for ARIES/IFE studies by relating these damages to heat deposition and neutron fluence.

Mirror Defects and Damage Types, andApproaches to Assess their Effects on Beam Quality

Dimensional Defects Compositional Defects

Gross deformations, δ>λ Surface morphoλogy, δ <λ Gross surfacecontamination

Locaλ contamination

CONCERNS

• Fabrication quaλity• Neutron sweλλing• Thermaλ sweλλing• Gravity λoaδs

• Laser-inδuceδδam age

• Thermom echanicaλδam age

• Transm utations• Buλk reδeposition

• Aerosoλ, δust &δebris

MODELLING TOOLS

Opticaλ δesign software Scattering by roughsurfaces (Kirchhoff)

Fresneλ muλti-λayersoλver

Scattering by particλes

0

0.2

0.4

0.6

0.8

1

0 0.05 0.1 0.15 0.2 0.25 0.3

Surface Contaminants Can Degrade Reflectivity

• Surface contaminants (such as carbon) on mirror protective coatings can alter reflectivity, depending on layer thickness and incident angle.

• Reflectivity is reduced with increasing contaminant thickness.• Effect of surface contaminant is diminished at gracing incidence.

Carbon film thickness (nm)

refle

cti v

i ty

q = 0o

20o

40o

60o

80o

λo = 532 nmAl2O3 coating (10 nm)Al mirror

d2=2 nmq = 0o

d2=2 nmq = 80o

d2=0q = 0o

d2=0q = 80o

λo = 532 nmCarbon film Al mirror

refle

ctiv

ity

Al2O3 coating thickness, d3/λo

Assessment Approach on Transmutation Effect

• Neutron irradiation of the mirror can cause transmutations of the protective coating and metal substrate, thus altering their optical properties.

• Assume the ambient material and transmutant have dielectric constant ea and eb, respectively, and volume fraction of transmutant is fb. Using the effective medium approximation (EMA), an effective eeff can be defined using the Bruggeman expression:

• The fraction fb is an increasing function of the neutron fluence.

• This model can be incorporated into the Fresnel solver to account for effect of transmutations on mirror reflectivity. However, need input from neutronics and information on transmutant dielectric properties.

0 =(1−fb) εa−εeffεa−2εeff

+fbεb−εeffεb −2εeff

Dimensional Defects Compositional Defects

Gross deformations, δ>λ Surface morphoλogy, δ <λ Gross surfacecontamination

Locaλ contamination

CONCERNS

• Fabrication quaλity• Neutron sweλλing• Thermaλ sweλλing• Gravity λoaδs

• Laser-inδuceδδam age

• Thermom echanicaλδam age

• Transm utations• Buλk reδeposition

• Aerosoλ, δust &δebris

MODELLING TOOLS

Opticaλ δesign software Scattering by roughsurfaces (Kirchhoff)

Fresneλ muλti-λayermoδ eλ

Scattering by particλes

Mirror Defects and Damage Types, andApproaches to Assess their Effects on Beam Quality

• Assuming no coupling between polarizations, scalar theory applies.

• In the presence of a scatterer, total field is given by

• According to Kirchhoff theory, is given by

where S0 is surface of scatterer and G(r,r0) is the full-space Green’s function.

• Approximations required for analytic results: - Plane wave incidence - Far-field approximation : r >> r0 - Integration over mean plane

- Constant reflection coefficient :

Wave Scattering from Random Rough Surfaces

ψ(r r ) =ψinc(r r )+ψsc(r r )

ψsc(r r )

ψsc(r) = ψ(r r 0 )∂G(r r ,r r 0)

∂n0−G(r r ,r r 0)

∂ψ(r r 0)

∂n0

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

S0∫ d

r S 0

R ≠R(x0,y0)dSm

dS0n0

surface

Mean plane

h(x0,y0)

• The average scattered (coherent) field is [Ogilvy]

where 4XY is area of mean plane, y0sc is field scattered

from smooth surface, k(kz) is the characteristic function of the rough surface

p(h) is the statistical height distribution, and c = cosq2(1+R)-cosq1(1-R), kx = (2p/λ)[sinq1-sinq2cosq3], ky = -(2p/λ)sinq2sinq3, kz = -(2p/λ)(cosq1+cosq2)

• y0sc is peaked at q2=q1 and q3=0 [specular reflection], and has a lobe-like

spectrum around this point.

At X/λ >>1, and Yλ >> 1, this lobe-like structure disappears and there is only reflection in the specular direction.

Scattered Coherent Field

q1q2

q3

z

x

ykinc ksc

ψsc =−ikeikr4πr 4XYcχ(kz) sinkxX

kxX⎛ ⎝ ⎜ ⎞

⎠ ⎟ sinkyY

kyY⎛ ⎝ ⎜

⎞ ⎠ ⎟ =χ(kz)ψ0

sc

χ(s) = p(h)eish−∞

∞∫ dh

q1q2

Overall Scattered Intensity from a “Gaussian” Rough Surface

• The diffuse (non-coherent) portion of the scattered field is averaged to zero. However, the diffuse scattered intensity is nonzero, and given by

• Our interest is focused on the specularly reflected coherent intensity Icoh, which is the component that is aimed at the target.

• We assume a Gaussian height distribution of the form where s is the rms height of the damaged surface. Thus, k(kz) = exp{-kz

2s2/2} .

• Overall scattered intensity is where g = (4pscosq1/λ)2

• The assumption of near-Gaussian surface statistics is valid for “those surfaces with a profile that is everywhere the result of a large number of local events, the results of which are cumulative. … Surfaces produced by engineering methods, such as turning, are less likely to possess Gaussian height statistics than those arising from natural processes, such as fatigue cracks or terrain.”[J.A. Ogilvy]. Laser-induced and thermomechanical damages may have Gaussian statistics if these are induced cumulatively.

Id = ψscψsc∗ − ψsc ψsc∗

p(h) = 1σ 2π exp − h2

2σ2⎛

⎝ ⎜

⎞ ⎠ ⎟

Isc =I0e−g+ Id

0 0.1 0.2 0.3 0.4 0.5

1.0

0.8

0.6

0.4

0.2

0

s λ

Specularly Reflected Intensity can be Degraded by Surface Roughness

De g

rada

tion

F ac t

o r, e

-g

Isc =I0e−g+ Idq1 = 80o

70o

60o

At q1 = 80o, sλ = 0.1,

e-g = 0.97.

• Grazing incidence is less affected by surface roughness.

• To avoid loss of laser beam intensity, s λ < 0.01.

SUMMARY & FUTURE PLANS

• Fresnel analysis of oxide-coated metal mirrors has been carried out using a 4-layer model and assuming smooth surfaces. - Surface contaminant can have impact on reflectivity, which is minimized by grazing incidence.

• Applying Kirchhoff theory and assuming Gaussian surface statistics, specularly reflected beam intensity can be degraded if s λ > 0.01, for grazing incidence . (s : rms surface height, q1 = 80o) - How does effect vary with different surface characteristics?

• Two future tasks:

(1) Use optical design software to assess gross deformation effects e.g., ZEMAX

(2) Use technique of wave scattering by particles to assess effects of local contaminants on mirror (and in fused silica wedges).