The Optics of
Grating Light
Valves
FYS4230
Håkon Sagberg, SINTEF
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The Optics of Grating Light Valves
„ Introduction to ”Grating Light Valves”
„ Crash course in optical diffraction theory
„ The grating light valve (GLV) display
„ Grating light valves for other applications
„ Spectroscopy
„ Displacement sensing
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Deformable Mirror
Device (DMD)
Grating light
valves (GLV)
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Two methods for steering light
Deflection
Diffraction
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The grating light valve (GLV)
„ Grating Light Valve
„
„
„
„
Electrostatically deflect ribbons
Distance to wafer λ/4
Light is reflected or diffracted
Diffracted light is projected to
screen
„ Possible to use pull-in or pullcontrol
„ Possible to have one row of
ribbon pixels only
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Diffraction from a grating light valve
d
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GLV used in a display device
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Diffraction of Light
Maxwell’s equations may be reduced to the
scalar wave equation.
n ∂U
∇U= 2 2
c ∂t
2
2
2
U may be any component of
vectors H and E
Assumptions: Linear, isotropic, homegeneous and nondispersive
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Diffraction of light
Example solutions of the wave equation are
the plane wave and spherical wave:
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Diffraction of light
Light bends or diffracts around edges. Small
apertures give large diffraction angles
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Diffraction of light
Light bends or diffracts around edges. Small
apertures give large diffraction angles
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Diffraction of light
Light bends or diffracts around edges. Small
apertures give large diffraction angles
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Diffraction of light
Here, edge effects are small
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Diffraction of light
When edges are thick and holes
are small, scalar diffraction theory
is no longer valid
???????
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The Huygens-Fresnel principle says:
”The light disturbance at a point P arises from the
superposition of secondary waves that proceed from a
surface situated between this point and the light
source.”
Augustin-Jean
Fresnel
Christiaan Huygens
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Diffraction of Light
A mathematical representation of the HuygensFresnel principle:
Spherical wave
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Diffraction of Light
Far away from the aperture, and for small
diffraction angles we may use the Fraunhofer
approximation.
U ( β ) = C ∫ U ( x) exp(ikβx)dx
S
x
β
S
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Diffraction of Light
Far away from the aperture, and for small
diffraction angles we may use the Fraunhofer
approximation.
U ( β ) = C ∫ U ( x) exp(ikβx)dx
S
x
β
S
Fourier transform!
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Diffraction of Light
We may now calculate the diffraction from a slit:
⎡ ⎛ kβa ⎞ ⎤
⎢ sin ⎜ 2 ⎟ ⎥
⎠⎥
I =⎢ ⎝
⎢ ⎛ kβa ⎞ ⎥
⎢⎣ ⎜⎝ 2 ⎟⎠ ⎥⎦
2π
k=
2
λ
a
β
Minima for:
β =m
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a
19
Babinet’s principle
The diffracted field from an
aperture is the same as from an
obscuration of the same size
and shape
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Diffraction from a grating light valve
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The grating equation
mλ
sin β ≈ β =
d
d
Phase difference = an integer number
of wavelengths
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Diffraction from a grating light valve
h
d
2
4
I
U
2
=
= 2 sin (kh)
I0 U0
π
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Diffraction from a grating light valve
Angle given by the grating equation
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Diffraction from a grating light valve
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How to design a GLV display device
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Different pixels for different wavelengths
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How to design a GLV display device
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Grating light valves
„ Can you spot the
difference between
the top and bottom
GLV?
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The clamped-clamped beam with
distributed load
0
-0.05
h(x)
-0.1
-0.15
-0.2
-0.25
-0.3
-0.35
-1
-0.8
-0.6
-0.4
Must integrate
diffraction efficiency
over the length of
the beam:
-0.2
0
0.2
0.4
0.6
0.8
1
I
4
= 2 ∫ sin 2 [kh( x)]dx
I0 π L
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How to design a GLV display device:
Challenges
„ High optical throughput requires large diffraction angle
and short grating periods
„ The shorter the period the more light is lost in the gaps
between the ribbons
„ Clamped-clamped beams/ribbons result in low fill factor
„ Only a fraction of the beam is optically useful
„ Different wavelengths require different modulation heights
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”Grating light valves” for spectroscopy
„ ”Polychromator”
„ SINTEF CDOE
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Polychromix/Senturia
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Polychromix (Senturia)
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SINTEF CDOE
„ Start with BSOI wafer with λ/4 (500nm) thick
buried oxide layer
„ Reactive Ion Etch (RIE) of the diffraction grating
„ Aluminum sputtering and annealing
„ Aluminum etch and DRIE (Bosch process) of
device layer
„ Oxide etch (release) using vapor phase HF
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SEM images of the fabricated device
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„ This animation shows the principle of a first-order grating light valve. Only a
narrow exit angle is considered.
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Our aim is to measure gas concentration using a
micromechanical infrared filter
The figure shows an old, established infrared
sensing method for measuring gas concentration
Image taken from Moseley et al,
”Techniques and mechanisms
in gas sensing”
Optical
MEMS device
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Reference measurements must be made in one or
more wavelength bands outside the absorbing region
„ Example: Carbon dioxide absorption
„ Single detector
Infrared transmittance
spectrum
of CO2
1000 ppm karbondiosyd og
vann, 50 cm
1
„ Alternating filter
0.9
0.8
0.7
Transmisjon
Detector signal
Abs.
Ref.
meas. meas.
0.6
0.5
0.4
0.3
No Gas
present
Gas
present
0.2
0.1
0
2150
2200
2250
2300
2350
2400
2450
2500
2550
-1
Time
Bølgetall [cm ]
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Design concept: Optical filtering
with Modulated diffraction gratings
„ Shine white light (broadband IR)
onto a diffraction grating
„ Collect the light diffracted into a
chosen angle
„ Change the color and intensity of the
light by electromechanical
modifications of the grating shape
„ Design objective:
„ Electromechanically simple
„ No position feedback
„ No calibration
„ No drift
„ Robust
„ Low-cost
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„ When used with wider grating elements, for diffraction order M=6, the
neighboring diffraction orders come closer...
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Actuation characteristic
Deflection vs. voltage
0
1
2
3
4
5
0
Deflection (nm)
-100
-200
Idle (0V)
-300
-400
Decreasing V
Increasing V
-500
Voltage (V)
„ Bistable operation with
snap-down at 4.2V
„ Hysteresis due to pull-in effect
Fully actuated (5V)
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0V
5V
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Infrared spectral characterization
MOEMS
Device
IR
Source
Light intensity on detector
Actuation voltage
1.7
1.8
1.9
2
2.1
2.2
2.3
0
3
Fiber to FTIR
spectrometer
20.1
10.1
4.7
4.5
4.3
4.1
3.9
3.7
3.5
3.3
Actuation voltage in V
Wavelength in μm
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”Grating light valves” for displacement
sensing (F.L. Degertekin)
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”Grating light valves” for displacement
sensing (F.L. Degertekin)
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