Elizabeth F. McCormackBryn Mawr College

Jean-Marc FournierInstitute of Imaging and Applied OpticsSwiss Federal Institute of Technology

Tomasz GrzegorczykMassachusetts Institute of Technology

Robert StachnikChristina River Institute

LaserLaser--Trapped Mirrors in SpaceTrapped Mirrors in Space

Liz McCormack

The LTM DesignThe LTM Design

TRAPPED MIRROR

Laser

Mirror

Star Light

CCD

Particle source

Mirror

Standing wave of laser light traps particles

(Labeyrie, A&A, 1979)(Labeyrie, A&A, 1979)

Liz McCormack

Attributes of the LTMAttributes of the LTMPotential for very large aperture mirrors with very low mass (35 m--> 100g !) andextremely high packing efficiency (35m--> 5 cm cube).

Resilience against meteoroid damage (self-healing).

Deployment without large moving parts,potential to actively alter the mirror’s shape, andthe flexibility to change mirror “coatings” in orbit. .

Potential for fabricating “naturally” co-phased arrays of arbitrary shape as shown at left.

The LTM should be diffraction limited at long wavelengths. For a trapping wavelength in the visible, e.g. 0.5 µm, and operation at 20 µm,the “flatness” of the mirror could be better than λ/80.

Liz McCormack

Laser Trapped Mirrors in SpaceLaser Trapped Mirrors in Space

ArtistArtist’’s view of Laser Trapped Mirrors view of Laser Trapped Mirror(NASA study by Boeing(NASA study by Boeing-- SVS)SVS)

Liz McCormack

Investigation of the Feasibilityof a Laser Trapped Mirror (LTM)

Part I: Experimental Status

JeanJean--Marc FournierMarc Fournier

Bryn Bryn MawrMawr CollegeCollegeandand

Imaging and Applied Optics InstituteImaging and Applied Optics InstituteSwiss Federal Institute of TechnologySwiss Federal Institute of Technology

October 17, 2006 NIAC meeting Tucson, AZ

Investigation of the feasibility of a LTM

Part I: experimental status

• Putting LTM in perspective

• Imaging properties

• Multiple trapping schemes

• Optical trapping and optical binding

• Conclusion and perspectives

• Conferences and publicationsJean-Marc Fournier

F

Refraction force.Hyakutake comet

a photon carries Energy and momentum.

E = c p

a photon carries Energy and momentum.

E = c p

Example of optical forces

Jean-Marc Fournier

Arthur Ashkinphotorefractive effect

four-wave mixing

optical levitation optical trapping

Arthur Ashkin, “Acceleration and trapping of particles by radiation pressure”, Phys. Rev. Lett. 24. 156-159, 1970

Arthur Ashkin, “Trapping of atoms by resonance radiation pressure”,Phys. Rev. Lett. 40. 729-732, 1978

A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,”

Optics Letters 11(5), pp. 288–290, 1986.

Every creative act is a sudden cessation of stupidity

Jean-Marc Fournier

Dipolar trap

Jean-Marc Fournier

Optical TrappingA. Ashkin, Acceleration and trapping of particles by radiation pressure,

Phys. Rev. Lett. 24. 156-159, 1970A. Ashkin, Trapping of atoms by resonance radiation pressure,

Phys. Rev. Lett. 40. 729-732, 1978

Fgrad

⟨Fgrad⟩ = ½ α . ∇⟨E2⟩

Fscat

⟨Fscat⟩ = 1/3 α2 k4 ⟨E2⟩

Dipoleapproximation

k4 = 1/cλ4

23

2

1α = a2

nn

−+

23

2

1α = a2

nn

−+

23

2

1α = a2

nn

−+

Jean-Marc Fournier

High Throughput Screening:High Throughput Screening:

Caliper LabCaliper Lab--onon--aa--Chip Technology at Chip Technology at SeronoSerono

Revolutionary Advance in Revolutionary Advance in Laboratory TechnologyLaboratory Technology

Miniaturization, Integration, AutomationMiniaturization, Integration, Automation

Map Discrete Workstations toMap Discrete Workstations tointegrated micro channelsintegrated micro channels

Alex Scheer

Jean-Marc Fournier

Laser532 nmPolystyrene :

refractive index: 1.59density: 1.05

Water :refractive index: 1.33frictioncooling/dissipation

Jean-Marc Fournier

Microscopes and Microscopes and TelescopesTelescopes

CCD

sample

Microscope

∑ob ∑ref

Its not that we need new ideas, but we need to stop having old ideas.

Edwin H. LandJean-Marc Fournier

Labeyrie’sLabeyrie’s VisionVisionStanding wave from laser light traps particles

Particle source

TRAPPED MIRROR

Star Light

CCD

Laser

Mirror

Mirror

A. Labeyrie, A&A, 1979-Marc Fournier

recording reconstruction

inverse propagation

Requires a flat recording wave…Requires a flat recording wave…….easier to make if somewhat convex….easier to make if somewhat convexNot a major problemNot a major problem Jean-Marc Fournier

From the microscope to the telescope?From the microscope to the telescope?

Compensation or annihilation of radiation pressure effect

Maintain a Maintain a parabolic structureparabolic structure

Neutral stateNeutral state(charges are screened)(charges are screened)

No frictionNo frictionDissipationDissipation

30° K30° Kcoolingcooling

In vacuumIn vacuumIn WaterIn Water

TrappingTrapping

Jean-Marc Fournier

Experiments in water _ Year IExperiments in water _ Year I

Work on different trapping Work on different trapping schemes in waterschemes in water

Best size achieved with a 5 Watt Best size achieved with a 5 Watt laser and micrometer laser and micrometer size particlessize particles

Prove experimentally that an Prove experimentally that an optical crystal works as a optical crystal works as a mirror mirror

Jean-Marc Fournier

An LTM in waterAn LTM in water

Self-organization in dipole trapsJean-Marc Fournier

Investigation of the feasibility of a LTM

Part I: experimental status

• Putting LTM in perspective

• Imaging properties

• Multiple trapping schemes

• Optical trapping and optical binding

• Conclusion and perspectives

• Conferences and publicationsJean-Marc Fournier

Mirror function: imaging and focusingMirror function: imaging and focusing

Jean-Marc Fournier

Mirror function: Imaging and focusingMirror function: Imaging and focusing

8

f

ff

f

DifferenceWhitout beadsarray

With beads array

Jean-Marc Fournier

Investigation of the feasibility of a LTM

Part I: experimental status

• Putting LTM in perspective

• Imaging properties

• Multiple trapping schemes

• Optical trapping and optical binding

• Conclusion and perspectives

• Conferences and publicationsJean-Marc Fournier

J.-M. Fournier, M.M. Burns, and J.A. Golovchenko, “Writing Diffractive Structures by Optical Trapping”, Proc. SPIE 2406 “Practical holography”, pp. 101-111, 1995.

M.M. Burns, J.-M. Fournier, and J.A. Golovchenko, "Optical Matter", US Patent # 5,245,466, 1993

Jean-Marc Fournier

NN--Beam interferenceBeam interferencearray of trapsarray of traps

template generation

intensity pattern

Piezo

imaging system

CCD

Jean-Marc Fournier

InterferometricInterferometric trap arraystrap arrays

2 Beams 3 Beams

20 20 µµmm 20 20 µµmm

2 2 µµmm4 4 µµmmJean-Marc Fournier

Creation of High Contrast FringesCreation of High Contrast Fringes

varying fringe spacingvarying fringe spacingSteep gradientsSteep gradients

Sample area

I

I∇sin

sin∇

Jean-Marc Fournier

Investigation of the feasibility of a LTM

Part I: experimental status

• Putting LTM in perspective

• Imaging properties

• Multiple trapping schemes

• Optical trapping and optical binding

• Conclusion and perspectives

• Conferences and publicationsJean-Marc Fournier

Optical binding force

Consider all fields:Incident and scattered,Near and far

Pair of oscillators:Driven by fields andradiating like dipoles

Solve self-consistency

Ek

B

Jean-Marc Fournier

Jean-Marc Fournier

Binding force

2 2 2binding

sin(kr)F =α k Ir

Scattering force

23

2

1α = a2

nn

−+

2 4scat

1

3F = α k I grad

1

2F α I= ∇

Gradient force

Net Force

Net Force

© J.M. FournierJean-Marc Fournier

Optical binding in dipolar trapOptical binding in dipolar trap

Jean-Marc Fournier

Self Self organizationorganization in a large in a large dipole trapdipole trap

Z=0 µm

Binding and trapping at different positions in a gaussian beam

Z=7500 µm Z=1250 µm

3 W

68 beads 199 beads 198 beads

1 W

64 beads 142 beads113 beads

3.5 µm polystyrene spheres Jean-Marc Fournier

Optical binding in dipolar trapOptical binding in dipolar trap

Jean-Marc Fournier

Mirror size: How large?Mirror size: How large?

Bead’s size 2 µmMirror diameter 90 µm

Bead’s size 3.5 µmMirror diameter 77 µm

@ 4 WattsJean-Marc Fournier

Mirror size: How large?Mirror size: How large?

Beads size 5 µmMirror diameter 135 µm

Beads size 6 µmMirror diameter 250 µm

@ 4 Watts

Jean-Marc Fournier

Trapped optical crystal. about 1500 beads (2 µm) in hexagonal traps

Diameter= 240 µm Jean-Marc Fournier

Optical BindingOptical Binding

Stability

Ground state?

Collective effect

Field enhancement

Jean-Marc Fournier

Fixing Trapped StructuresFixing Trapped StructuresFrom dynamic systems to hard copies::

Build efficient diffractive opticsConstruct customized phase functions

J.-M. R. Fournier, M.M. Burns, and J.A. Golovchenko, “Writing Diffractive Structures by Optical Trapping”, SPIE Proceed. 2406, 101-111, 1995

2.9 µm polystyrene spheres

in a polyacrylamidehydrogel

Do we want polymerization or isomeration?

What about self –healing property ?

Jean-Marc Fournier

Collaborators VisionCollaborators Vision

?bert Stachnik

Antoine LabeyrieLTM Collaborators Meetings

- Cambridge, MA, March 2006- Lausanne, CH, July 2006

Jean-Marc Fournier

Collaborators publications related to LTMCollaborators publications related to LTM

M. Guillon, "Field Enhancement in a Chain of Optically Bound Dipoles“, Opt. Express 14, 3045-3055, 2006.

M. Guillon, O. Moine, and B. Stout, “Longitudinal Optical Binding of High Optical Contrast Microdroplets in Air”, Phys. Rev. Lett. 96, 143902, 2006.

M. Guillon, “Optical Binding in Air”, PIERS 2006 Cambridge, 2006.

G.L. Lippi, S. Barland, M. Colombet, J. Farmer, R. Kaiser, and J.-M. Fournier, “Light-Mediated Particle Interactions in a Laser Trap”, PIERS 2006 Cambridge, 2006.

O. Moine and B. Stout, “Exact Calculations of Optical Forces and Optical Binding in Single and Multiple Beam Optical Traps”, PIERS 2006 Cambridge, March 29, 2006.

A. Labeyrie and J.-M. Fournier , “Interférometers and hypertelescopes”, , tribute to P.M. Duffieux and J. Duvernoy, GDR Ondes, Besançon, France, Nov 2005.

A. Labeyrie, M. Guillon and J.-M. Fournier, “Optics of “Laser Trapped Mirrors” for large telescopes and hypertelescopes in space”, SPIE Proc. 5899, 2005.

G.L. Lippi, R. Kaiser, N. Mönter, T. Chanelière, J.-M. Fournier, «Optical binding: a scattering-mediated force arising in micro-and nanoscopic samples”, Proc. European Quantum Electronics Conference, Munich, 2005.

O. Moine, “Modelisation de Forces Optiques”, PhD thesis, Marseille, Nov. 2005. Jean-Marc Fournier

Diffusion regimesDiffusion regimes

0.1λ 10λ

Dipolar modelRigorous

electromagnetic calculation

Geometric optics

characteristic dimensionsof diffusing object

diffusion model

Use a size parameter ka, with:

a: object size .k: wave number of incident beam

ka 0.6 60

O. Moine, PhD Thesis, Marseille, 2005 Jean-Marc Fournier

Investigation of the feasibility of a LTM

Part I: experimental status

• Putting LTM in perspective

• Imaging properties

• Multiple trapping schemes

• Optical trapping and optical binding

• Conclusion and perspectives

• Conferences and publicationsJean-Marc Fournier

Different trapping schemesDifferent trapping schemes

Optical binding in dipolar trapOptical binding in dipolar trap

InterferometricInterferometric trap arraystrap arrays

MultipleMultiple--beam interferencebeam interference

Fresnel diffraction / Talbot imagingFresnel diffraction / Talbot imaging

Jean-Marc Fournier

Need for better understanding of Need for better understanding of binding and on optical forcesbinding and on optical forces

How far the 1/r force can be carried on? Watch out for How far the 1/r force can be carried on? Watch out for polarization!polarization!

Is it a configuration for which binding would help to Is it a configuration for which binding would help to «« growgrow » the mirror by field enhancement?» the mirror by field enhancement?

Jean-Marc Fournier

ThankThank You !You !Jean-Marc Fournier

Investigation of the feasibility of a Investigation of the feasibility of a laser trapped mirror (LTM)laser trapped mirror (LTM)Part II: theory and modelingPart II: theory and modeling

Tomasz M. GrzegorczykTomasz M. Grzegorczyk

October 17th, 2006NIAC 8th annual meeting

Tuscon, Arizona

Center for Electromagnetic Theory and ApplicationsCenter for Electromagnetic Theory and ApplicationsResearch Laboratory of ElectronicsResearch Laboratory of ElectronicsMassachusetts Institute of TechnologyMassachusetts Institute of Technology

Tomasz M. Grzegorczyk

BackgroundBackgroundLaser beams

Gaussian Bessel

Scattering force

Gravitation

Gradient force

Summers et al., “Optical guiding of aerosol droplets”, Optics Express, 14(14), 2006.

Initial references:

•Ashkin, “Acceleration and trapping of particles by radiation pressure”, PRL 1970.•Ashkin and Dziedzic, “Optical levitation by radiation pressure”, APL 1971.•Ashkin and Dziedic, “Radiation pressure on a free liquid surface”, PRL 1973.•Ashkin and Dziedic, “Optical levitation of liquid drops by radiation pressure”, Science 1975.

Image: Prof. J.-M. Fournier

Tomasz M. Grzegorczyk

Laser beams

Gaussian Bessel

Scattering force

Gravitation

Gradient force

Summers et al., “Optical guiding of aerosol droplets”, Optics Express, 14(14), 2006.

Initial references:

•Ashkin, “Acceleration and trapping of particles by radiation pressure”, PRL 1970.•Ashkin and Dziedzic, “Optical levitation by radiation pressure”, APL 1971.•Ashkin and Dziedic, “Radiation pressure on a free liquid surface”, PRL 1973.•Ashkin and Dziedic, “Optical levitation of liquid drops by radiation pressure”, Science 1975.

Image: Prof. J.-M. Fournier

Tomasz M. Grzegorczyk

“The stuff of beams”, New Scientist, 13 May 2006.

Mellor and Bain, “Array formation in evanescent waves”, ChemPhysChem 7, 2006.

LASERLASER

Trapping in multiple beams

Source: Prof. J.-M. Fournier, Swiss Federal Institute of Technology, Lausanne, Switzerland.

Tomasz M. Grzegorczyk

Laser Trapped Mirror (LTM)Laser Trapped Mirror (LTM)

TRAPPED MIRROR

Laser

Mirror

TRAPPED MIRROR

MirrorMirror

Star LightStar Light

CCDCCD

Particle sourceParticle source

MirrorMirror

Concept: Artistic view:

Labeyrie, Astron. Astrophysics 77, 1979.

Advantages (extraordinary)• Arbitrarily large apertures • Exceptionally low areal mass• Self-healing properties• In space deployment• high packaging efficiency• etc

Difficulties (extraordinary)• Damping in free-space• Laser power, coherence• Single fringe trapping• Resist to space environment• Discharge of the dish• etc

Tomasz M. Grzegorczyk

Laser Trapped Mirror (LTM)Laser Trapped Mirror (LTM)

TRAPPED MIRROR

Laser

Mirror

TRAPPED MIRROR

MirrorMirror

Star LightStar Light

CCDCCD

Particle sourceParticle source

MirrorMirror

Concept: Electromagnetic view:

Labeyrie, Astron. Astrophysics 77, 1979.

Advantages (extraordinary)• Arbitrarily large apertures • Exceptionally low areal mass• Self-healing properties• In space deployment• high packaging efficiency• etc

Difficulties (extraordinary)• Damping in free-space• Laser power, coherence• Single fringe trapping• Resist to space environment• Discharge of the dish• etc

Tomasz M. Grzegorczyk

Electromagnetic modelingElectromagnetic modeling

Scattering force Gradient force Binding force

The force is unique, obtained from the Maxwell stress tensor or Lorentz force

Need accurate electromagnetic modeling

The field is much more mature from an experimental point of view than from a theoretical/numerical point of view.

Tomasz M. Grzegorczyk

Theoretical and numerical workTheoretical and numerical work

Compute the total EM fields in a single-body and multi-body systemsCompute the force on each bodyDeduce the dynamics of the system and look for interesting properties.

Challenges:

Multi-body systems: computing the exact EM fields might be very difficult.

Resort to 2D particles (cylinders) and the Foldy-Lax multiple scattering eqns.

Electrodynamics: density, viscosity, Brownian motion need to be accounted for.

Brownian motion is neglected so far (future work), systems are assumed over-damped (true for water, not true for free-space).

Controversies: lossy media, separation of fields and matter,

Develop a theory that is consistent with momentum conservation, Maxwellstress tensor, and Lorentz force (still being discussed in 2005).

Laser Trapped Mirror

Image formation by scattering from particles, study image quality.

Tomasz M. Grzegorczyk

Field scattering by an infinite cylinderField scattering by an infinite cylinder

Field expressions: Cylindrical modes:

Force expression:

Tomasz M. Grzegorczyk

Two particles:

N particles:Total exciting field onparticle j ; solved e.g.by matrix inversion

Scattered field from particle j

Scattered field from N particle

Total field including all interactions

Principle of Principle of FoldyFoldy--Lax equationsLax equations

Tomasz M. Grzegorczyk

Trapping in various sets of Trapping in various sets of sinusoidal trapssinusoidal traps

Source: Prof. J.-M. Fournier, Swiss Federal Institute of Technology, Lausanne, Switzerland

Tomasz M. Grzegorczyk

Three incidences

Matching experimentsMatching experiments

Tomasz M. Grzegorczyk

Two incidences

Matching experimentsMatching experiments

Tomasz M. Grzegorczyk

Two incidences

Matching experimentsMatching experiments

Tomasz M. Grzegorczyk

Three incidences

Matching experimentsMatching experiments

Tomasz M. Grzegorczyk

• Pure electromagnetic approach• Minimum approximations• Multiple particles in a parabola• Cylinders instead of spheres

Issues:• Size of models• Scaling properties• Feasibility

Einc

2D LTM simulations

Parameters: a=0.3λ, 81 cylinders

Full-wave simulations show a clear focusingfrom even a small number of particles

Tomasz M. Grzegorczyk

0.4 deg 0.8 deg 1.2 deg 1.6 deg 1.8 deg

2.0 deg 2.2 deg 2.4 deg 2.8 deg 3.2 degФD

1 realization

Monte Carloover 100realization

Parabola equation:

Resolution study

Surface roughness

Tomasz M. Grzegorczyk

Future of LTM modelingFuture of LTM modeling

Our modeling tool gives us a tremendous flexibility to study various geometries of LTMs:

• rough• separated particles• piecewise LTM• effects of “lost particles”

Piecewise LTM

Main issue: scale of the LTM

Separated LTM

Need to find a better algorithm or reasonable assumptions in order to be able to simulate ameter-size LTM.

Tomasz M. Grzegorczyk

ConclusionsConclusions

Important advancements have been done during Year 1:

Understanding of forces in media:Agreement between Lorentz force and Maxwell stress tensor for lossless/lossy media.

Modeling dynamics of 2D particles in an optical latticeExact calculation of fields and forces in complex systems.

Modeling of an LTM:

Demonstration of focusing using exact scattering calculationsStudy of resolution for two incident plane wavesStudy of image quality as function of roughnessNew possibilities for modeling large-scale LTM

Year 2: further modeling and feasibility study of the LTM

Tomasz M. Grzegorczyk

Publications under NIAC sponsorshipPublications under NIAC sponsorship

• Brandon A. Kemp, Tomasz M. Grzegorczyk, and Jin Au Kong, “Ab initio study of the radiation pressure on dielectric and magnetic media”, Optics Express, vol. 13, no. 23, 9280-9291, 14 November 2005.

• Brandon A. Kemp, Tomasz M. Grzegorczyk, and Jin Au Kong, “Lorentz force on dielectric and magnetic particles”, J. of Electromagn. Waves and Appl., vol. 20, no. 6, 827-839, 2006.

• Tomasz M. Grzegorczyk, Brandon A. Kemp, and Jin Au Kong, “Stable optical trapping based on optical binding forces”, Phys. Rev. Lett. 96, 113903, 2006.

• Tomasz M. Grzegorczyk, Brandon A. Kemp, and Jin Au Kong, “Trapping and binding of an arbitrary number of cylindrical particles in an in-plane electromagnetic field”, J. Opt. Soc. Am. A, 23(9) Sept. 2006.

• Brandon A. Kemp, Tomasz M. Grzegorczyk, and Jin Au Kong, “Optical momentum transfer to absorbing Mie particles”, Phys. Rev. Lett., 97(133902), 2006.

• Tomasz M. Grzegorczyk, Brandon A. Kemp, and Jin Au Kong, “Passive guiding and sorting of small particles with optical binding forces”, Opt. Lett., 31(22), Nov. 2006.

Journal papers:

Others:

• “Recent advances in optical trapping and binding”, conference session organized by Prof. J.-M. Fournier and Dr. T. M. Grzegorczyk, Prog. In Electromagn. Research Symp., Cambridge MA, March 26-29, 2006.

• “Optical matter, modeling and experimental realizations”, conference session organized by Prof. J.-M. Fournier and Dr. T. M. Grzegorczyk, Prog. In Electromagn. Research Symp., Beijing China, March 26-30, 2007.

• “The stuff of beams” J. Mullins, New Scientist, 13 May 2006.• “Controlling optical binding creates trap for optical matter”, PhyOrg.com, March 22, 2006.

Tomasz M. Grzegorczyk

“The stuff of beams”, New Scientist, 13 May 2006.Tomasz M. Grzegorczyk