Download Properties of Multilayer Optics

Properties of
Multilayer Optics
An Investigation of Methods of
Polarization Analysis for the ICS
Experiment at UCLA
8/4/04
Oliver Williams
Outline
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Purpose
Review of Polarization/Analysis in Visible
EUV/Soft x-ray Behavior in Materials
Basics of Multilayer Optics
ML Optics as Polarizers/Phase Retarders
Summary
Purpose
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Beam electrons scattering off CO2 laser
photons (~0.12 eV) expected to produce
~110 eV photons
Scattered photons assume polarization
state of laser photons = circular for ICS
experiment
Require analyzer capable of determining
degree of polarization of soft x-rays
Review of Polarization
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A preferential orientation of the electric field along a single axis
perpendicular to the direction of propagation= Linearly polarized
When the horizontal and vertical components of electric field are 90
degrees out of phase= Circularly polarized
At a boundary of different index of refraction (e.g. air-glass):
Horizontal = s-component (E-field perpendicular to plane of
incidence)
Vertical = p-component (E-field parallel to plane of incidence)
Brewster’s Angle: Angle at which the s-component of the E-field is
completely reflected while the p-component is completely absorbed
or transmitted; dependent on the index of refraction of material.
tan  1(nr )  
Br
Some Methods of
Polarization/Analysis
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Dichroic/Wire grid polarizers – Linear
Brewster’s angle based – Linear
Birefringence (crystals) – Linear & Circular
1/4 wave plates – Circular
Of particular interest to the ICS experiment are analyzers based on
quarter wave plates due to their ability to retard (or advance) the
relative phases of the s and p components of the electric field by 90
degrees (ideally).
The well-known method of using a ¼ wave plate followed by a linear
polarizer as an analyzer can be used to determine the degree of
circular polarization of the scattered photons.
However…
EUV/Soft X-ray Behavior in Materials
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The real part of the refractive index (nr) of materials seen by light in
the EUV/SXR (>30 eV approx.) approaches unity as the energy
increases. The complex refractive index is,
n~  1    i
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where δ is the decrement of the real part of the refractive index and
β is the absorption index with both typically very small (<10-3) for
this energy.
This makes conventional optics almost useless, except at
grazing/glancing angles (θ<5 deg), as the amplitude reflectivity of a
surface for EUV/SXR ranges 1/30 to 1/100.
Basics of Multilayer Optics
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If the reflections of 30-100 surfaces can be
arranged such that their phases interfere
constructively at the top surface, a total
reflectivity close to one can be achieved.
Bragg condition: Light reflecting off many
surfaces will be strongly dependent on the
distance between reflection layers (d) and the
angle of incidence (θ) as the total distance
traveled must be an integer number (m) of
wavelengths (λ) to constructively interfere and
is given by the equation,
m  2d sin(  )
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The dependence of the reflectivity on the
wavelength of light makes ML optics inherently
good filters
ML Optics as Linear Polarizers
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Because the index of refraction for EUV/SXR light is close to
one, Brewster’s angle is near 45 degrees.
Adjusting the spacing between layers (d) in the Bragg
equation one can place this Bragg reflection peak also near
45 degrees
This causes the ML optic to be highly reflective (due to the
multilayer reflections) and especially to the s-component
since the angle of maximum reflection is at Brewster’s angle
This makes ML optics almost perfect linear polarizers as the
relative reflection (transmission) between the s and p
components is very large (small).
http://www-cxro.lbl.gov/optical_constants/multi2.html
ML Optics as Phase Retarders
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There already exist modest phase
shifts between the s and p
components at dielectric/vacuum
interfaces at certain angles of
incidence, however because the
reflectivity is so low it is inefficient
to be used as a retarder.
Graphs to the right show the
reflectance of the s and p
components of 90 eV photons on
a Molybdenum mirror as a
function of incidence angle as well
as the (normalized) relative phase
shift, Δφ.
Adding multilayers changes the
optical properties around Bragg
peak, especially.
Reflection Retarders
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As seen from the plots, phase
retardation based on reflection can
be quite effective, producing Δφ≈45
degrees.
Because of the necessity of
operating near 45 degrees for
decent phase shifts, the reflectivity
of the p-component is quite low
(≤0.1), which is extended to
≤0.01(two reflections) if it is to
function as a ¼ wave plate.
Besides the inefficiency, the
introduction of one more optical
element to align, especially under
vacuum and only receiving a signal
every few minutes (for us), makes
reflection retarders difficult to use.
Transmission Retarders
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Essentially same fabrication
process as reflection type
except necessity of removing
substrate by etching gives
higher surface roughness.
However, the transmission
retarder is able to achieve
Δφ≈90 degrees between s
and p on only one pass with
about the same efficiency as
one reflection.
This is made possible by the
modulation of the electric field
between the low and high
absorption regions of the ML.
Transmission vs. Reflection
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Upon strong reflection off a layer a standing
wave is formed which effectively changes the
refractive index felt by the total field.
If the Bragg peak is placed near Brewster’s
angle, only the s-component feels this
electric field modulation and change in
refractive index which causes a phase shift
with respect to the p-component.
The effect of this modulation in the
transmission case (top graph) is compared to
reflection and it can be seen in the plots that
the normalized phases of the s and p
components in transmission more strongly
“slip” past each other at certain angles than
for reflection.
Because this change in phase is so heavily
dependent on strong E-field modulation, and
hence strong reflection, poorly fabricated
transmission ML’s are much less forgiving in
phase shifts than reflection ML’s.
Summary
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Multilayer optics are excellent small bandwidth filters
Reflective linear polarizers based on ML’s are very effective
in the EUV/SXR region
¼ wave plates based on transmissive multilayers have
shown to be more efficient and practical than the reflection
type
Sensitivity to imperfections make the fabrication of
transmission ML’s more difficult and (most likely) more
expensive than reflection ML’s
An x-ray detector in combination with a transmission retarder
and reflection analyzer (polarizer) mounted on vacuum
compatible motorized rotation stages could be used to verify
the circular polarization of the ICS photons at Neptune