Gaussian to Super-Gaussian Intensity Profile Conversion with Refractive Micro-Optics

$Page 1: Gaussian to Super-Gaussian Intensity Profile Conversion with Refractive Micro-Optics$
Gaussian to Super-Gaussian Intensity Profile Conversion with Refractive Micro-Optics

Justin Mansell, Todd Rutherford, Bill Tulloch, MichaelOlapinski, Martin M. Fejer, and Robert L. Byer

Edward L. Ginzton LaboratoryStanford University

NSF Contract 2WMF572

Justin Mansell - [email protected] University

Outline• Motivation - LIGO• Introduction

– Thermal Lensing– Super-Gaussians

• Converter Design• Micro-Optic Fabrication• Laboratory Results• Conclusion


Research Motivation

• Laser Interferometer Gravitational-Wave Observatory (LIGO)– Modified Michelson Interferometer with 4000 meter long arms

pumped with10W of 1064nm Nd:YAG CW laser light.

Livingston Site

Hanford Site


The LIGO Interferometer• LIGO interferometer

consists of many optical cavities.

• Optimal coupling to these cavities requires high beam quality.

• Beam quality can be reduced by thermal lensing in thetransmissive optics before the interferometer like the– Faraday isolator– electro-optic

modulator


What are Super-Gaussians?• The functional form

of a continuous transition from a gaussian to a top-hat.

Super-Gaussian Profiles

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2r/w

Nor

mal

ized

Inte

nsity

Gaussian3rd Order4th Order5th Order6th Order

Gaussian( )

��

�

�

��

�

�−=

n

wr

IrI 2exp0

r - radius.w - super-gaussian waistn - super-gaussian order (>2)


Why Super-Gaussians?• Better extraction from saturated laser

amplifiers.• Better non-linear conversion for same

peak intensity.• Top-hat beams have a parabolic

thermal lens which does not decrease beam quality.


What is Thermal Lensing?• Slight absorption in

transmissive optics causes heating.

• Non-uniform heating creates non-uniform temperature distribution.

• Temperature variation causes slight change in refractive index.

Absorbing Material

Laser

thkq

T−=∇2

)()()( rTdTdn

LrnLr ∆⋅⋅≈∆⋅≈∆Λ

T - temperatureq - heat sourcekth - thermal conductivityr - radiusdn/dT - thermo-optic coefficientΛ - optical path length


Gaussian Thermal Lens Shape-4

-2

0

2

4

6

8

10

12

14

0 0.5 1 1.5 2Radius / Waist

Dis

torti

on (w

aves

)

Thermal LensOptimal Parabolic CompensationDifference

��

�

�

��

�

�

��

�

��

��

�+��

�

��

��

�+Γ=∆Λ22

22ln4

)(wr

Ewr

dTdn

kP

r ith

absorbed

π

Thermal Lens Magnitude =Magnitude of Distortion at1/e2 Intensity Radius


Calculated Effect of Gaussian Thermal Lens on Laser Beam Quality

00.10.20.30.40.50.60.70.80.9

1

0 0.5 1 1.5 2Thermal Lens Magnitude (waves)

Pow

er C

oupl

ing

TEM00 with focus compensation

TEM00 without focus compensation




Top-Hat Thermal Lensing for LIGO

• Top-Hat intensity profiles have an exactly parabolic thermal lens profile in heated region and logarithmic tails.

• Advantages:– Parabolic thermal lenses can be compensated with simple

optical systems.– Do not need complex adaptive optics system.

• Disadvantage:– Top-Hat beams do not couple much light into LIGO

interferometer.

• Ideally we want top-hat through optics and gaussian into interferometer.


Ideal Converter Implementation

TransparentConverter

ReflectiveCompensator

To Interferometer

From Laser

TransmissiveOptics


Refractive Optic Converter Design

• Used ray optics to obtain shape– Divided input & output

into equal energy pieces and remapped.

• Limitations:– Only perfect super-

gaussian in one plane.

– Difficult profile to obtain without complex fabrication techniques.

Converter Shape

Output Profile

Input Profile


Super-Gaussian Converter Fabrication

Spin AZ4620 photoresistonto a fused silica wafer.

Pattern the photoresistinto circular pillars.

Expose the wafer to acetonevapor for about 5 minutes.

Put the wafer into an anisotropic plasma etcher that etchesphotoresist and fused silica at similar rates.

After all thephotoresist is removed, the optic is ready for use.

3D Rendering


Fabrication Results

Converter Optic Surface

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

-600 -300 0 300 600Position(microns)

Hei

ght (

mic

rons

)

Measured

Fit to 4th-OrderPolynomial


System Performance

• Initial Beam Mx2=1.02 & My

2=1.05• Super-G Beam Mx

2=2.33 & My2=2.28

• Gaussian Beam Mx2=1.10 & My

2=1.08

NPROLaser

Ring Mode Cleaner

Lens 2Converter

Compensator


Super-Gaussian Profile

Super-Gaussian Profile

00.10.20.30.40.50.60.70.80.9

1

-1800 -800 200 1200Radius(um)

Inte

nsity

(au)

DataFit


Super-Gaussian Propagation

2

3

4

5

6

7

8

9

10

250 300 350 400Distance (mm)

Ord

er

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Wai

st S

ize

(mm

)


0

200

400

600

800

1000

1200

0 500 1000 1500Radius (um)

dOP

L (n

m)

0

0.2

0.4

0.6

0.8

1

1.2

Nor

mal

ized

Inte

nsity

6th Order SG

Gaussian Measured Super-GaussianThermal Lens & Parabolic Fit(RMS Error = 0.8nm)

Measured Gaussian Thermal Lens & Parabolic Fit(RMS Error = 6.7nm)

Thermal Lens Profiles

NOTE: Parabolic Fits done to 99% power radius.


Conclusions• We have built a simple converter-

compensator pair to generate a super-gaussian intensity profile from a gaussian beam by reflowing photoresist.

• The same type of converter was used in reflection to convert the super-gaussian beam back to a gaussian beam.

• The thermal lensing is exclusively parabolic and can be compensated by a simple lens system.


Shack-Hartmann Wavefront Sensor

Lens Array CCD Array

ZX

Y

IncidentWavefront

Light Focussing

Reference Positions (black circles)

Measured Positions(clear circles)

∆ x

∆ y

x

y

CCD Array Behind a Single Lens

Gaussian to Super-Gaussian Intensity Profile Conversion with Refractive Micro-Optics

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