LIGO-G050218-00-LIGO-G050218-00-ZZ

Gaussian to Super-Gaussian to Super-Gaussian Diffractive Gaussian Diffractive Optical Elements Optical Elements Patrick LuPatrick LuAdvisor: Prof. Robert ByerAdvisor: Prof. Robert ByerStanford UniversityStanford UniversityMarch 23, 2005March 23, 2005

IntroductionIntroduction

Goals:Goals: Laser beam shaping for increased power extraction Laser beam shaping for increased power extraction

from slab amplifiers in master oscillator power amplifier from slab amplifiers in master oscillator power amplifier systemssystems Gaussian to super-Gaussian conversion to extract more power Gaussian to super-Gaussian conversion to extract more power

from wings of beamfrom wings of beam Gaussian to super-Gaussian conversion to allow larger beams Gaussian to super-Gaussian conversion to allow larger beams

while still avoiding clipping (steeper roll-off)while still avoiding clipping (steeper roll-off)

Future LIGO arms may contain resonant mesa beams.Future LIGO arms may contain resonant mesa beams. Top-hat beam will be more efficient in stimulating this modeTop-hat beam will be more efficient in stimulating this mode

LIGO-G050218-00-LIGO-G050218-00-ZZ

Beam Shaping ProblemBeam Shaping ProblemInput to amplifiers is, at the moment, gaussianInput to amplifiers is, at the moment, gaussian

Diffraction limits size of beamDiffraction limits size of beamLarger beams cause ringing in the outputLarger beams cause ringing in the output

Small beam size means that only power from center of slab is Small beam size means that only power from center of slab is extractedextracted

Top Hat beam would fill a larger portion of the slab, extracting Top Hat beam would fill a larger portion of the slab, extracting power from the outside portion of the slabpower from the outside portion of the slab

Slabs are rectangular—a square or rectangular top-hat is preferred over roundSlabs are rectangular—a square or rectangular top-hat is preferred over round

Computing the Required Computing the Required Phase ProfilePhase Profile

Amp

Phase

The Gerchberg-Saxton algorithm was used to compute the phase that, when applied to a Gaussian, yields a 7th-order super-Gaussian in the fourier domain.

Computing the Required Computing the Required Phase Profile (2)Phase Profile (2)

The phase on the last slide will take a Gaussian and turn it into a super-The phase on the last slide will take a Gaussian and turn it into a super-Gaussian in the far-field. Gaussian in the far-field.

+ =

Phase from Gerchberg-Saxton + converging lens = ideal DOE phaseie, the DOE contains the near-field phase and a converging lens which willcreate an FT plane

Changing the x-scaling of the near-field phase changes the x-scaling of the supergaussian (they are inversely related). Changing the power of the lens changes the location of the fourier plane. These two variables create a two-dimensional space of possible ideal DOE phases.

FabricationFabrication

Acetone vapor

Plasma etch

Photoresist is patterned using standard photolithography.

After a short exposure to acetone, the photoresist reflows.

The shape of the photoresist is transferred to the quartz substrate with a CF4 and O2 plasma etch.

Two types of DOEs were fabricated: those that convert on ONE axis, and those that convert on BOTH axes. This picture shows the linear DOEs.

Fabrication (2)Fabrication (2) For the linear DOEs, two back-to-back optics, orthogonal to For the linear DOEs, two back-to-back optics, orthogonal to

each other, are required for conversion on both the x- and each other, are required for conversion on both the x- and y-axes, creating square supergaussiany-axes, creating square supergaussian

Silicate bonding

Results for Linear DOE’sResults for Linear DOE’s

Measured 1-D profile and simulated resultsMeasured 1-D profile and simulated results

Zygo Measurements + Zygo Measurements + Simulation of Linear Simulation of Linear DOE’sDOE’s

Simulation of having Simulation of having profile in both ‘x’ and profile in both ‘x’ and ‘y’‘y’

5% rms variation in 5% rms variation in “flat-top” portion“flat-top” portion

Physical realization Physical realization requires two DOE’s, requires two DOE’s, one ‘x’, one for ‘y’one ‘x’, one for ‘y’

Square DOE’sSquare DOE’sDesired Phase

Measured Optic (using Zygo)

Simulation Results

ExperimentalExperimental

Beam size (roughly Beam size (roughly 700 to 800 microns)700 to 800 microns)

DOE contains a built-in DOE contains a built-in converging lensconverging lens

External lens and built-External lens and built-in lens determine in lens determine location of fourier location of fourier planeplane

Camera needs to be Camera needs to be placed at fourier planeplaced at fourier plane

WinCamDDOE (contains converging lens)

lens

40W 30WTEM00

Mode-cleaner

Spot Size vs. Propagation Spot Size vs. Propagation for Collimated Outputfor Collimated Output

Curvature of Curvature of incident incident Gaussian Gaussian (750mm ROC) (750mm ROC) has been has been adjusted to adjusted to provide provide collimated ouputcollimated ouput

b

dr

Figure of merit: Figure of merit: normalized rise-normalized rise-distance (derived distance (derived from the trapezoidal from the trapezoidal approximation)approximation)

From 45mm to 95mm From 45mm to 95mm the beam profile is a the beam profile is a viable top-hatviable top-hat

Target slab has an Target slab has an effective length of effective length of 6cm/1.82 = 3.3cm6cm/1.82 = 3.3cm

Normalized rise-distance = dr/b

Top-Hat Quality vs. Top-Hat Quality vs. PropagationPropagation

Future WorkFuture Work

Make better diffractive optical elementsMake better diffractive optical elements Customize the size of the optic for Shally’s amplifier Customize the size of the optic for Shally’s amplifier

(.9mm x 1.11mm). Consider making asymmetrical (.9mm x 1.11mm). Consider making asymmetrical DOEsDOEs

Achieve a more accurate profile with squareish Achieve a more accurate profile with squareish DOEs.DOEs.

Create an optic which will convert back from Create an optic which will convert back from the super-Gaussian profile.the super-Gaussian profile.

Experiment with an available amplifier to show Experiment with an available amplifier to show improved extraction.improved extraction.

ConclusionsConclusions

DOEs have been fabricated which convert DOEs have been fabricated which convert 700700µm-diameter Gaussian beams into µm-diameter Gaussian beams into comparable-sized super-Gaussian beamscomparable-sized super-Gaussian beams

The super-Gaussian beams have lateral The super-Gaussian beams have lateral dimensions which are close to that of slab dimensions which are close to that of slab amplifiers, and retain their top-hat shape for amplifiers, and retain their top-hat shape for 5cm, which exceeds the effective length of 5cm, which exceeds the effective length of many amplifiers.many amplifiers.

A similar process may yield round top-hat A similar process may yield round top-hat beams which can efficiently stimulate cavities beams which can efficiently stimulate cavities with mexican-hat mirrors.with mexican-hat mirrors.