Quantum Optical Coherence Tomography

Transcription

1 Quantum Optical Coherence Tomography Bahaa Saleh Alexander Sergienko Malvin Teich Quantum Imaging Lab Department of Electrical & Computer Engineering & Photonics Center QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. MURI 6/9/05 1

2 Quantum Optical Coherence Tomography = Axial imaging (ranging) by use of: 1) 2-photon light in an entangled state, 2) a quantum interferometer, 3) a photon coincidence detector Source Interferometer x Detector Sample MURI 6/9/05 2

3 Outline 1. Two-Photon Imaging 2. QOCT: Prior Work 3. New Results MURI 6/9/05 3

4 Outline 1. Two-Photon Imaging 2. QOCT: Prior Work 3. New Results MURI 6/9/05 4

5 Two-Photon light σ 1 k 1 k q X=(q,ω,σ) spatial spectral polarization σ 2 k 2 = a state of exactly two photons in multimodes (spatial/spectral/polarization) Ψ = dx 1 dx 2 ϕ( X 1,X ) 2 1 X1, 1 X2 non-separable function entangled state Entanglement: Spatial (momentum) Spectral Polarization MURI 6/9/05 5

6 Measurement of Two-Photon light ϕ x C = ϕ ( X 1,X 2 ) 2 dx 1 dx 2 ϕ X 1,X 2 ( ) obeys propagation laws of coherence function (Wolf s equations), although it is not a coherence function MURI 6/9/05 6

7 Two Configurations for Metrology / Imaging H r A. Direct ϕ x ϕ s C H o B. Interferometric H r ϕ s ϕ ϕ d H o x C H = Spatial, spectral, or polarization system ϕ (X,X ) = 1 d ϕ(x 1,X 2 ) ϕ(x 2,X 1 ) MURI 6/9/05 7

8 A. Applications of Direct 2-Photon Imaging ϕ s ϕ x C H o 1. Absolute Measurement 2. Ghost Imaging (transverse) x C 2-photon absorber 3. 2-Photon Microscopy (transverse) 4. 2-Photon Lithography (transverse) MURI 6/9/05 8

9 B. Applications of Interferometric 2-Photon Imaging H r ϕ s ϕ x C H o C = 1 4 ϕ(x 1,X 2 ) ϕ(x 2,X 1 ) 2 dx 1 dx 2 QOCT MURI 6/9/05 9

10 Outline 1. Two-Photon Imaging 2. QOCT: Prior Work 3. New Results MURI 6/9/05 10

11 Axial Imaging/Ranging Spectral Modes H r (ω) ϕ s ϕ x C H o (ω) ϕ s (ω 1,ω 2 )= F(ω 1 )δ(ω 1 +ω 2 ω p ) H r (ω)= e iωτ ϕ(ω 1,ω 2 )= H r (ω 1 )H o (ω 2 )F(ω 1 )δ(ω 1 +ω 2 ω p ) C = 1 4 ϕ(ω 1,ω 2 ) ϕ(ω 2,ω 1 ) 2 dω 1 dω 2 Interference term in C H o (ω 1 )H o * (ω 2 ) e i(ω 1 ω 2 )τ δ(ω 1 +ω 2 ω p )F(ω 1 )F * (ω 2 ) i.e., insensitive to even-order dispersion (GVD) in H o, MURI 6/9/05 11

12 Q-OCT cτ H(ω) x C(τ) z C(τ ) 2Λ(0) 2Re{ Λ(2τ )} Λ( τ)= dωh (ω o +Ω) H * (ω o Ω)S(Ω)e iωτ C(τ) Dispersion-Cancellation τ Hong-Ou-Mandel Interferometer Abouraddy et al. PRA, , 2002 MURI 6/9/05 12

13 Experimental Setup for Hybrid OCT & QOCT cτ Detector 55 mw 2.2 mm Filter x C(τ) NLC 8-mm LiIO 3 Filter Detector Kr nm Sample I(τ) Nasr et al. PRL, 91, August 2003 MURI 6/9/05 13

14 Two Boundaries + dispersive layer 5-mm ZnSe Air 90 μm fused silica Air 53 μm Classical Quantum 19 μm MURI 6/9/05 14

15 Four Boundaries + dispersive medium in-between NORM. QOCT C (τ q ) NORM. OCT I (τ c ) μm AIR FW HM = 19.3 um Vis.=9% FWHM = 104 um Vis.=7.2% mm ZnSe β s 2 m -1 FWHM = 35.5 um AIR 90-μm FWHM = 18.5 um Vis.=27.5% FWHM = 37 um Vis.=23% PATH DELAY c τ / 2 (μ m) M. B. Nasr et al., Opt. Express 12, (2004) MURI 6/9/05 15

16 Four Boundaries + dispersive medium in-between MURI 6/9/05 16 M. B. Nasr et al., Opt. Express 12, (2004)

17 Outline 1. Two-Photon Imaging 2. QOCT: Theory & Prior Experimental Work 3. New Results MURI 6/9/05 17

18 Goals Design and build new QOCT system with performance competitive with OCT for acquisition of dispersioncancelled B-scan images Improve efficiency (reduced run time) Improve axial resolution Include transverse effects & nonplanar samples Approach New source (PPLN) Sergienko New detectors ( ) Improved layout (miniaturization) Study of transverse effects MURI 6/9/05 18

19 Minitiarization Standard: C DS = 1.3 m Mini: DM = 0.6 m C MURI 6/9/05 19

20 Transverse Effects Single reflector sample OCT Scan of Mirror Sample Normalized Single Counts Focusing in Conventional OCT Lens in sample & reference arms Position (mm) Lens in Sample Arm Only Lenses in Sample and Reference Arms Lens in sample arm only MURI 6/9/05 20

21 Focusing in QOCT Single reflector sample Lens in sample arm Different filter No Lens mm MURI 6/9/05 21

22 Compensation using two lenses in reference arm MURI 6/9/05 22

23 Depth of Focus DSM Variation of Axial Position of Sample Mirror in Dual 4-f Lens System in QOCT Vary Position of Mirror (DSM) Visibility of HOM Dip Sample Mirror Displacement from Ideal Alignment DSM (microns) Detector Pinholes = open; FWHM = 13 microns MURI 6/9/05 Pinholes = 4mm; FWHM = 15 microns 23 Pinholes = 2.5mm; FWHM = 19 microns

24 QOCT with Chirped-QPM Crystal After Carrasco et al., Opt. Lett. 29, (2004) MURI 6/9/05 24

25 Experimental Demonstration of Submicron OCT Spectral Width FWHM (nm) Counts 12 x μm Path Delay(μm) Counts 6 x μm Path Delay(μm) Pump Beam Width (microns) Non-Collinear Angle, 9.1º Counts 6 x μm Path Delay(μm) MURI 6/9/

26 The Promise of Q-OCT Q-OCT promises x2 improved axial resolution in comparison with conventional OCT for sources of same spectral bandwidth Self-interference at each boundary is immune to GVD introduced by upper layers Inter-boundary interference is sensitive to dispersion of interboundary layers; dispersion parameters can thus be estimated Preliminary experiments demonstrated viability of technique Technique can be extended to transverse imaging (Q-OCM) Technique can be extended to polarization-sensitive Q-OCT MURI 6/9/05 26

27 Q-OCT: Challenges & Plans State-of-the-art linewidth is not sufficiently large (Axial resolution is only 19 μm). Two-photon flux is low. Duration of experiment is too long. A better 2-photon source is needed! Faster broadband single-photon detector is needed! Applications to scattering media (e.g., tissue). Theoretical & experimental research is necessary. Algorithms for data processing need to be developed. MURI 6/9/05 27