Optical Vortex Coherence Filter Lt Col Gregory Foo, USAF (Ret) Grover A. Swartzlander, Jr. Optical Sciences Center University of Arizona Tucson, AZ David Palacios JPL Support US Army Research Office (ARO)

Overview Research Objectives Definitions Math Model Experiments Results Applications

Research Objectives Assess optical vortex coherent filtering –Is it feasible? –Effects on imaging –Alternative interference filter?

Definitions Coherent Light - Uniform phase (e.g. laser) Incoherent Light - Random phase (sunlight) Optical Vortex (OV)- Phase singularity/ defect –Undefined Phase –Zero Amplitude –Localized Destructive Interference Optical Vortex Phase Mask –Transmissive Corkscrew –Forms an OV

OV Math Model Helical Wavefront m = 3 E(r, ,z)  A(r,z)exp[ im´( )  exp[  ikz] A(r,z)- Amplitude m´( )  Topological Charge  Phase k  2   kTkT k

Mutual Coherence  (r 1, r 2,  ) =  (r 1, t +  )  * (r 2, t )  –(Coherent) 1 >  > 0 (Incoherent) y r1r1 r2r2 x

 d= [(m  )/2  (n 0 - 1)], 0    2  ∆d OV Phase Mask Continuous Discrete

Laser Filtering Object Lens Beam Splitter Image Phase Mask Laser CCD Camera Z X 330 cm33 cm 0.4 cm ∆z

Laser Filtering Mixed CoherenceOV Filtering Low Coherence

LASER VORTEX ARRAY DETECTOR VORTEX ELEMENT Sensor Protection

OV Point Spread Function High CoherenceLow Coherence Pixel

OV Coronagraph ksks kpkp  Vortex Mask x fofo z D

OV Coronagraph Calculated Pinhole Star

White Light OV Propagation 1 < z < 400 waves

Broadband Filtering 6.11>m´>4.15  P/P = 6.7 (10 -4 ) 2.03>m´>1.38  P/P = 3.2(10 -2 )

OV Core Properties ~ Point size in the focal plane Core/Beam increases with z Core/beam nearly constant for large z. Phase mask displacement controls size Approaches size of Airy disk Darkness increases with spatial coherence Nulls spatially coherent light

OV Applications Sensor Protection Exoplanet Detection Image Processing Optical Communication Optical Tweezers

Fourier Propagation exp (im´  )

C n Dependence on m

OV Propagation Point Source m = waves 1.53 > m´ > 1.34