Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake...
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Transcript of Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake...
![Page 1: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/1.jpg)
Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top
Beam Shaper
Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top
Beam Shaper
Blake Anderton
Mon, Dec. 8 2008
![Page 2: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/2.jpg)
The BIG problem …The BIG problem …
• Overview: gain medium illuminated as shown.
Veryexpensive
lasergain
mediumf
Fourier-conjugate planes
![Page 3: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/3.jpg)
The BIG problem …The BIG problem …
• Common input: circularly symmetric Gaussian
Veryexpensive
lasergain
mediumf
Gaussian input
Gaussian output
![Page 4: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/4.jpg)
The BIG problem …The BIG problem …
• Result: Strange and
not-so-wonderful things happen.
Veryexpensive
lasergain
mediumf
Gaussian input
Gaussian output
Too much light at center(scoring, crack)
(also not good)
Too little light at edge
(lost opportunity)
(not good)
![Page 5: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/5.jpg)
But what if…But what if…
…you modify the input beam’s phase to produce a uniform (“flat-top”, “circ”) pattern at gain medium?
Veryexpensive
lasergain
medium
Gaussian input
UNIFORMoutput beam (!)
Benefits of uniform beam at gain medium • no scoring (too much light)• no missed gain opportunities at edges (too little light)
?
Phase plate(ei scaling factor)
![Page 6: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/6.jpg)
The “ideal” … The “ideal” …
• Phase plate produces “Bessinc” entering lens• Output: “perfect” circ in Fourier plane
Gaussian input
?
Phase plate
“Bessinc” “Circ”
![Page 7: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/7.jpg)
The “ideal” …& why it costs too much
The “ideal” …& why it costs too much
• Phase plate produces “Bessinc” entering lens• Output: “perfect” circ in Fourier plane• Requires: continuous-phase plate (high
precision etching)
Gaussian input
$$$
CONTINUOUS-phase plate
“Bessinc” “Circ”
![Page 8: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/8.jpg)
How to mimic a BessincHow to mimic a Bessinc
• Compare plate input and ideal output– Input:
Gaussian– Output: Bessinc
• Key difference: y-values (pos/neg)
BEFORE phase plate
AFTER phase plate (ideal)
?Gauss Bessinc
![Page 9: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/9.jpg)
How to mimic a BessincHow to mimic a Bessinc
• Where do first negative Bessinc values occur (radially)?
• We designate that ring’s width by w.
ww
![Page 10: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/10.jpg)
How to mimic a BessincHow to mimic a Bessinc
• Where do first negative Bessinc values occur (radially)?
• We designate that ring’s width by w.
• Add remaining bands with approx. same width w
ww
w
w
w
w
![Page 11: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/11.jpg)
How to mimic a BessincHow to mimic a Bessinc
• Make Gaussian values negative within these bands.
• Result is negative where Bessinc is negative.
ww
w
w
w
w
![Page 12: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/12.jpg)
How to mimic a BessincHow to mimic a Bessinc
• Net result (right):– Not quite Bessinc – better than Gaussian.
• With this going into the lens, how do we build a phase plate to make this?
?
Goes here
![Page 13: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/13.jpg)
How do we make this phase plate?How do we make this phase plate?
• We seek to specify in ei.• What values must take?
![Page 14: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/14.jpg)
• We seek to specify in ei.• What values must take?
– Everything btwn 0 and 2
How do we make this phase plate?How do we make this phase plate?
![Page 15: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/15.jpg)
• We seek to specify in ei.• What values must take?
– Everything btwn 0 and 2– Just 0 or (inside/outside the
bands).
How do we make this phase plate?How do we make this phase plate?
![Page 16: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/16.jpg)
• We seek to specify in ei.• What values must take?
– Everything btwn 0 and 2– Just 0 or (insdie/outside the
bands).
• How to produce these ’s?– Etch a substrate (index n)
height profile h(r) such that
= 0 or
How do we make this phase plate?How do we make this phase plate?
![Page 17: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/17.jpg)
How many bands do we really need?How many bands do we really need?
• At right: effect of 1st, 2nd bands
• Bands 2+ have minimal effect.
Effect of 1st band
(BIG)
Effect of 2nd band
(less than big)
What if phase plate ONLY had 1 band (no 2nd, 3rd, …)?
![Page 18: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/18.jpg)
• Plot: comparing 1-, 2-, 3-band plates.
• Result: Not too different!
• Bottom line: only 1 band is needed.
Don’tneed
Don’tneed
Don’tneed
Don’tneed
Don’tneed
Don’tneed
How many bands do we really need?How many bands do we really need?
![Page 19: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/19.jpg)
How far are we from ideal? 3 Figures of Merit (FOMs)
How far are we from ideal? 3 Figures of Merit (FOMs)
• How do you compare the Fourier-plane field produced by a binary-phase plate to the “ideal” circ? With 3 figures-of-merit:
– Uniformity: “ringing” in central zone (less ringing is better)
Plot of typical Fourier-plane
intensity produced by single-banded
binary-phase plate
Central zone is defined as having
intensity ≥ 90% peak
![Page 20: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/20.jpg)
How far are we from ideal? 3 Figures of Merit (FOMs)
How far are we from ideal? 3 Figures of Merit (FOMs)
• How do you compare the Fourier-plane field produced by a binary-phase plate to the “ideal” circ? With 3 figures-of-merit:
– Uniformity: “ringing” in central zone (less ringing is better)
– Steepness: slope of central-zone boundary (steeper is better)
Plot of typical Fourier-plane
intensity produced by single-banded
binary-phase plate
Central zone is defined as having
intensity ≥ 90% peak
![Page 21: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/21.jpg)
How far are we from ideal? 3 Figures of Merit (FOMs)
How far are we from ideal? 3 Figures of Merit (FOMs)
• How do you compare the Fourier-plane field produced by a binary-phase plate to the “ideal” circ? With 3 figures-of-merit:
– Uniformity: “ringing” in central zone (less ringing is better)
– Steepness: slope of central-zone boundary (steeper is better)
– Efficiency: energy spread beyond central-zone (less loss is better)
Plot of typical Fourier-plane
intensity produced by single-banded
binary-phase plate
Central zone is defined as having
intensity ≥ 90% peak
![Page 22: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/22.jpg)
Check with experimentCheck with experiment
• System characteristics– = 633 nm (wavelength)– = 420 m (Gaussian e-1 radius and
inner-radius r0 of single phase-plate zone)
– f = 200 mm (lens focal length)– d = 184 mm (obs. plane location)– = 0.8768 (phase on a h = 0.52
m, n = 1.534 single-zone, binary-phase plate)
Value of d was changed to compensate the departure in etch depth h (designed for 0.47 um, actually got 0.52 um)
![Page 23: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/23.jpg)
Check with experimentCheck with experiment
• Comparing predicted/actual results:
– Predicted• Uniformity: U = 2.2%• Steepness: K = 0.61• Efficiency: = 75%
– Actual• Uniformity: U < 3%• Steepness: K = 0.59• Efficiency: = 72.3%
Experi-mental
results: Intensity along x-
direction
Experi-mental
results: Intensity along y-
direction Good agreement!
![Page 24: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/24.jpg)
SummarySummary• Driving problem: non-uniform beam at gain medium.
• Costly ideal: continuous-phase plates.
• Affordable alternative: binary-phase modification of a
Gaussian’s similarity to “ideal” (circ-producing) Bessinc
• Manufacturing: relating phase level to etch depth h in a
substrate of index n
• Simplifying: marginal benefits of more than one zone
• Figures-of-merit: uniformity, steepness, efficiency
• Verification: through experiment
![Page 25: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/25.jpg)
ConclusionConclusion
Single-zone, binary-phase plates provide an affordable, mechanically-feasible option for
producing a uniform field in an optical system’s focal plane.
![Page 26: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/26.jpg)
Relevance to OptomechanicsRelevance to Optomechanics
• Provides mechanically-feasible “phase grating” implementation.
• Exemplifies a system with mechanical compensation capability (d,).
• Yang/Wang also include tolerancing examples: zone width, etch depth sensitivities at +/- 10% of design values.
• Exemplifies cost benefits of designing for manufacturability (1-zone vs. 2+).
![Page 27: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/27.jpg)
Thank you!Thank you!
![Page 28: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/28.jpg)
How far are we from ideal? 3 Figures of Merit (FOMs)
How far are we from ideal? 3 Figures of Merit (FOMs)
• How do you compare the Fourier-plane field produced by a binary-phase plate to the “ideal” circ? With 3 figures-of-merit:
Plot of typical Fourier-plane
intensity produced by single-banded
binary-phase plate
Central zone is defined as having
intensity ≥ 90% peak
![Page 29: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/29.jpg)
Selecting observation distance d and phase for optimum FOMs
Selecting observation distance d and phase for optimum FOMs
• Now, best d and depend on FOMs: U, K, .– They’ll differ from (d = f, ).
• If we set d = f,
we need
• If we set ,
we need d = 0.81f
d = f
0.79
25
d =0.81 f
Bes
t F
OM
s
Bes
t F
OM
s
![Page 30: Synopsis of Yang/Wang’s Analysis and Optimization on Single-Zone Binary Flat-Top Beam Shaper Blake Anderton Mon, Dec. 8 2008.](https://reader035.fdocuments.in/reader035/viewer/2022062301/5697bfab1a28abf838c9afa1/html5/thumbnails/30.jpg)
Check with experiment
• System characteristics– = 633 nm (wavelength)– = 420 m (Gaussian e-1 radius and
inner-radius r0 of single phase-plate zone)
– f = 200 mm (lens focal length)– d = 184 mm (obs. plane location)– = 0.8768 (phase on a h = 0.52
m, n = 1.534 single-zone, binary-phase plate)
Value of d was changed to compensate the departure in etch depth h (designed for 0.47 um, actually got 0.52 um)