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Multi-Photon and Entangled-Photon Imaging and Lithography
Malvin Carl TeichCollege of Optics & PhotonicsUniversity of Central Florida
Columbia & Boston Universities
http://people.bu.edu/teich
University of Virginia
Physics Colloquium7 October 2011
Photonics CenterBoston University
Photons Arrive Randomly
Δn Δφ = 1/2 Product of photon-number and phase uncertainties:
Multiphoton Excitationvs
Entangled-Photon Excitation
For classical light, probability of simultaneous absorption ofn photons ∝ I n
Multiphoton absorption more likely in regions of high light intensityUltrafast light pulses have high peak
intensities, allowing multiphotonexcitation at low average powerExcitation (photoemission, fluorescence,
lithography, photochemistry), can be localized for n photonsFor entangled-n-photon light, probability
of simultaneous absorption of n photons ∝ I
Optics & Photonics News 11, 40 (2000)
Generation of Entangled Photon Pairs via Spontaneous Parametric Down-Conversion
Laser χ(2)
Crystal
Signal
Idler
Pump
kp ωp σp
ks ωs σs
ki ωi σi
ωp = ωs + ωiENERGY CONSERVATION:
MOMENTUM CONSERVATION: kp = ks + ki
kp
kski
After Joobeur, Saleh, and Teich, “Spatiotemporal Coherence Properties of Entangled Light Beams Generated by Parametric Down-Conversion," Phys. Rev. A 50, 3349 (1994)
PHOTONS ARE EMITTED IN PAIRS (TWINS): IDEAL REAL•Each at a random time, but times are correlated :•Each is broadband, but frequencies are anti-correlated :•Each is multidirectional, but directions are anti-correlated :•Each with random polarization, but polarizations are orthogonal : (Type-II SPDC)
consts i et t τ τ τ− = = Δ ≡consts i p pω ω ω ω+ = = Δconsts i p eA+ = = Δ ≡k k k k
MultiphotonMultiphotonAbsorptionAbsorption
T: T: GGööppertppert--Mayer (1931)Mayer (1931)E: Franken E: Franken et alet al. (1961). (1961)
PhotoemissionPhotoemissionT: Bloch (1964)T: Bloch (1964)E: Teich & E: Teich & WolgaWolga (1964)(1964)
MicroscopyMicroscopyT: Sheppard & T: Sheppard & KompfnerKompfner (1978)(1978)E: E: DenkDenk et al.et al. (1990)(1990)
LithographyLithographyT: ancientT: ancientE: 3D..Maruo & E: 3D..Maruo & KawataKawata (1997)(1997)
OCT OCT (Optical Coherence (Optical Coherence Tomography Tomography –– Single Photon)Single Photon)
T: T: YoungquistYoungquist et alet al. (1987). (1987)E: Huang E: Huang et alet al. (1991). (1991)
EntangledEntangled--PhotonPhotonAbsorptionAbsorption
T: T: FeiFei et al.et al. (1997)(1997)E: Dayan E: Dayan et al.et al. (2004)(2004)
PhotoemissionPhotoemissionT: T: LissandrinLissandrin et al.et al. (2004)(2004)E:E:
MicroscopyMicroscopyT: Teich & Saleh (1997)T: Teich & Saleh (1997)E:E:
LithographyLithographyT: T: BotoBoto et al.et al. (2000) (2000) E:E:
QOCT QOCT (Quantum Optical (Quantum Optical Coherence Tomography Coherence Tomography –– 22--Photon)Photon)
T: T: AbouraddyAbouraddy et al.et al. (2002) (2002) E: E: NasrNasr et al.et al. (2003)(2003)
EXAMPLES
MultiphotonMultiphotonAbsorptionAbsorption
T: T: GGööppertppert--Mayer (1931)Mayer (1931)E: Franken E: Franken et alet al. (1961). (1961)
PhotoemissionPhotoemissionT: Bloch (1964)T: Bloch (1964)E: Teich & E: Teich & WolgaWolga (1964)(1964)
MicroscopyMicroscopyT: Sheppard & T: Sheppard & KompfnerKompfner (1978)(1978)E: E: DenkDenk et al.et al. (1990)(1990)
LithographyLithographyT: ancient T: ancient E: 3D..Maruo & E: 3D..Maruo & KawataKawata (1997)(1997)
OCT OCT (Optical Coherence (Optical Coherence Tomography Tomography –– Single Photon)Single Photon)
T: T: YoungquistYoungquist et alet al. (1987). (1987)E: Huang E: Huang et alet al. (1991). (1991)
EntangledEntangled--PhotonPhotonAbsorptionAbsorption
T: T: FeiFei et al.et al. (1997)(1997)E: Dayan E: Dayan et al.et al. (2004)(2004)
PhotoemissionPhotoemissionT: T: LissandrinLissandrin et al.et al. (2004)(2004)E:E:
MicroscopyMicroscopyT: Teich & Saleh (1997)T: Teich & Saleh (1997)E:E:
LithographyLithographyT: T: BotoBoto et al.et al. (2000) (2000) E:E:
QOCT QOCT (Quantum Optical (Quantum Optical Coherence Tomography Coherence Tomography –– 22--Photon)Photon)
T: T: AbouraddyAbouraddy et al.et al. (2002) (2002) E: E: NasrNasr et al.et al. (2003)(2003)
EXAMPLES
Second-Harmonic Generation (SHG)
Enhancement of SHG via Thermal Light or Speckle
Entangled-Photon Absorption (Theory)
After Fei, Jost, Popescu, Saleh, and Teich, "Entanglement-Induced Two-Photon Transparency," Phys. Rev. Lett. 78, 1679 (1997)
Entangled-Photon SFG (Experiment)
After Dayan, Pe’er, Friesem, and Silberberg, “Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons,”
Phys. Rev. Lett. 94, 043602 (2005)
Linear OpticsLinear OpticsScalarScalar
SuperSuper--resolutionresolution
Vector beamVector beam
Nonlinear OpticsNonlinear OpticsPhase conjugationPhase conjugation
STED STED (stimulated (stimulated emission depletion emission depletion microscopy)microscopy)
MultiphotonMultiphotonimagingimaging
NONLINEAR AND ENTANGLED-PHOTON IMAGING
Quantum OpticsQuantum OpticsQuadratureQuadrature--squeezed imagingsqueezed imaging
NumberNumber--squeezedsqueezedimagingimaging
EntangledEntangled--photon photon imagingimaging
c
Distortingmedium
Mirror
Optical Imaging = Extracting the spatial distribution of a remoteobject (static or dynamic, 2D or 3D, scalar or vector, B/W or color).
MultiphotonMultiphotonAbsorptionAbsorption
T: T: GGööppertppert--Mayer (1931)Mayer (1931)E: Franken E: Franken et alet al. (1961). (1961)
PhotoemissionPhotoemissionT: Bloch (1964)T: Bloch (1964)E: Teich & E: Teich & WolgaWolga (1964)(1964)
MicroscopyMicroscopyT: Sheppard & T: Sheppard & KompfnerKompfner (1978)(1978)E: E: DenkDenk et al.et al. (1990)(1990)
LithographyLithographyT: ancientT: ancientE: 3D..Maruo & E: 3D..Maruo & KawataKawata (1997)(1997)
OCT OCT (Optical Coherence (Optical Coherence Tomography Tomography –– Single Photon)Single Photon)
T: T: YoungquistYoungquist et alet al. (1987). (1987)E: Huang E: Huang et alet al. (1991). (1991)
EntangledEntangled--PhotonPhotonAbsorptionAbsorption
T: T: FeiFei et al.et al. (1997)(1997)E: Dayan E: Dayan et al.et al. (2004)(2004)
PhotoemissionPhotoemissionT: T: LissandrinLissandrin et al.et al. (2004)(2004)E:E:
MicroscopyMicroscopyT: Teich & Saleh (1997)T: Teich & Saleh (1997)E:E:
LithographyLithographyT: T: BotoBoto et al.et al. (2000) (2000) E:E:
QOCT QOCT (Quantum Optical (Quantum Optical Coherence Tomography Coherence Tomography –– 22--Photon)Photon)
T: T: AbouraddyAbouraddy et al.et al. (2002) (2002) E: E: NasrNasr et al.et al. (2003)(2003)
EXAMPLES
PULSEDLASER
FLUORESCENCESIGNAL
LENS
ADVANTANGES: Longer wavelength source penetrates more deeply into tissue. Excitation only occurs only at focal region – eliminates pinhole detectors, increases SNR, and provides optical sectioning capabilities.
DISADVANTAGES: Large photon flux is required. Samples must have broad upper-energy levels. Expensive titanium:sapphire laser system. Sample photodamage.
ADVANTANGES: Guaranteed photon pairs create comparable depth penetration but at substantially reduced light levels. Samples do not require broad upper-energy levels. Pump laser can be continuous-wave or pulsed.
DISADVANTAGES: Overall photon flux is low. Entangled-photon absorption cross-section and entanglement area are not well established.
Multiphoton Microscopy
INCIDENTPHOTONS
SAMPLE
LENS
NONLINEAR CRYSTAL
LASER
Entangled-Photon Microscopy
After Teich and Saleh, "Mikroskopie s kvantově provázanými fotony (Entangled-Photon Microscopy),"Československý časopis pro fyziku 47, 3 (1997)U.S. Patent 5,796,477 (issued 18 August 1998)
MultiphotonMultiphotonAbsorptionAbsorption
T: T: GGööppertppert--Mayer (1931)Mayer (1931)E: Franken E: Franken et alet al. (1961). (1961)
PhotoemissionPhotoemissionT: Bloch (1964)T: Bloch (1964)E: Teich & E: Teich & WolgaWolga (1964)(1964)
MicroscopyMicroscopyT: Sheppard & T: Sheppard & KompfnerKompfner (1978)(1978)E: E: DenkDenk et al.et al. (1990)(1990)
LithographyLithographyT: ancientT: ancientE: 3D..Maruo & E: 3D..Maruo & KawataKawata (1997)(1997)
OCT OCT (Optical Coherence (Optical Coherence Tomography Tomography –– Single Photon)Single Photon)
T: T: YoungquistYoungquist et alet al. (1987). (1987)E: Huang E: Huang et alet al. (1991). (1991)
EntangledEntangled--PhotonPhotonAbsorptionAbsorption
T: T: FeiFei et al.et al. (1997)(1997)E: Dayan E: Dayan et al.et al. (2004)(2004)
PhotoemissionPhotoemissionT: T: LissandrinLissandrin et al.et al. (2004)(2004)E:E:
MicroscopyMicroscopyT: Teich & Saleh (1997)T: Teich & Saleh (1997)E:E:
LithographyLithographyT: T: BotoBoto et al.et al. (2000) (2000) E:E:
QOCT QOCT (Quantum Optical (Quantum Optical Coherence Tomography Coherence Tomography –– 22--Photon)Photon)
T: T: AbouraddyAbouraddy et al.et al. (2002) (2002) E: E: NasrNasr et al.et al. (2003)(2003)
EXAMPLES
Entangled-Photon Lithography (Theory)
After Boto, Kok, Abrams, Braunstein, Williams, and Dowling, “Quantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit,” Phys. Rev. Lett. 85, 2733 (2000)
Origin of factor of 2 resolution enhancement and validity for arbitrary masks:
Example: Radical MultiphotonAbsorption Polymerization
•Multiphoton absorption by a photo-initiator in a viscous liquid pre-polymer resin generates radicals. (A co-initiator may be required as well.)
•Photoexcitation of the photo-initiator begins a chain reaction that hardens the resin locally.
•Theoretical resolution available via multiphoton absorption (MPA) inversely proportional to the numerical aperture.
•Chemical nonlinearity (quenching of radicals by oxygen or recombination) can lead to a substantial increase in resolution via thresholding.
3D Lithography
After Baldacchini, LaFratta, Farrer, Teich, Saleh, Naughton, and Fourkas, “Acrylic-Based Resin with Favorable Properties for Three-Dimensional Two-Photon Polymerization,”
J. Appl. Phys. 95, 6072 (2004)
10 μm
After Farrer, LaFratta, Li, Praino, Naughton, Saleh, Teich, and Fourkas, “Selective Functionalization of 3-D Polymer Microstructures,” J. Am. Chem. Soc. 128, 1796 (2006).
1 µm
MultiphotonMultiphotonAbsorptionAbsorption
T: T: GGööppertppert--Mayer (1931)Mayer (1931)E: Franken E: Franken et alet al. (1961). (1961)
PhotoemissionPhotoemissionT: Bloch (1964)T: Bloch (1964)E: Teich & E: Teich & WolgaWolga (1964)(1964)
MicroscopyMicroscopyT: Sheppard & T: Sheppard & KompfnerKompfner (1978)(1978)E: E: DenkDenk et al.et al. (1990)(1990)
LithographyLithographyT: ancientT: ancientE: 3D..Maruo & E: 3D..Maruo & KawataKawata (1997)(1997)
OCT OCT (Optical Coherence (Optical Coherence Tomography Tomography –– Single Photon)Single Photon)
T: T: YoungquistYoungquist et alet al. (1987). (1987)E: Huang E: Huang et alet al. (1991). (1991)
EntangledEntangled--PhotonPhotonAbsorptionAbsorption
T: T: FeiFei et al.et al. (1997)(1997)E: Dayan E: Dayan et al.et al. (2004)(2004)
PhotoemissionPhotoemissionT: T: LissandrinLissandrin et al.et al. (2004)(2004)E:E:
MicroscopyMicroscopyT: Teich & Saleh (1997)T: Teich & Saleh (1997)E:E:
LithographyLithographyT: T: BotoBoto et al.et al. (2000) (2000) E:E:
QOCT QOCT (Quantum Optical (Quantum Optical Coherence Tomography Coherence Tomography –– 22--Photon)Photon)
T: T: AbouraddyAbouraddy et al.et al. (2002) (2002) E: E: NasrNasr et al.et al. (2003)(2003)
EXAMPLES
Classical Optical Coherence Tomography (OCT)OCT = Interferometric reflectometry using a broadband
source of light (short coherence length)
I(τ)
BroadbandSource
cτ
Detector
Sample
Mirror
1I(τ)
τ
Classical
SLD
Axial resolution is often of the order of a few μ mSubmicron resolution is possible with fs lasers and supercontinuum lightIn a dispersive medium, the resolution deteriorates to tens of μ m
See Youngquist, Carr, and Davies, “Optical coherence-domain reflectometry: A new optical evaluation technique,” Opt. Lett. 12, 158–160 (1987).
Laser Pump
Quantum Optical Coherence Tomography (QOCT)
Advantages of QOCT:Factor of 2 improvement in axial resolution for same spectral width Insensitivity to group-velocity dispersion w. concomitant improvement in axial resolution
C(τ)
z
cτ
Detector 2
Sample
Mirror
xNLC
Detector 1
C(τ)
τ
Laser PhotonCoincidence
= OCT based on quantum interferometry of spectrally-entangled photons generated by downconverted light from a nonlinear crystal
After Abouraddy, Nasr, Saleh, Sergienko, and Teich, “Quantum-Optical Coherence Tomography with Dispersion Cancellation,” Phys. Rev. A 65, 053817 (2002)
Note that coincidence detection achieves high visibility despite unbalanced loss
Optics Express, 12, 1353 (2004)
Indistinguishability Yields Interference
Source of simultaneously emitted photon pairs
Beamsplitterinterferometer
There are four possible photon paths at the beamsplitter: RT, TR, RR, and TT. For indistinguishable photons, the RR and TT alternatives cancel by virtue of the phase shift at the beamsplitter. The remaining RT and TR alternatives yield both photons exiting the same port of the beamsplitter (they appear to stick together) so that the probability of photon coincidence is zero.
NonlinearCrystal
Laser
xPhoton
coincidence
Detector
z Detector
R R
x
C(z)
z0
zNonlinear
Crystal
Laser
Detector
Detector
Photon coincidence
Pathlength difference
T TCANCELS
C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987)
RESULTING IN:
After Nasr, Saleh, Sergienko, and Teich, “Dispersion-Cancelled and Dispersion-Sensitive Quantum Optical Coherence Tomography,” Opt. Express 12, 1353 (2004)
Dispersion-Free QOCT (Experiment)
Q-OCT promises improved axial resolution in comparison with conventional OCT for sources of same spectral bandwidth
Source bandwidth for Q-OCT governed by process of entangled-photon generation (e.g., crystal width); can be tuned
Self-interference at each boundary immune to group-velocity dispersion introduced by layers above
Inter-boundary interference sensitive to dispersion of inter-boundary layers; dispersion parameters can thus be estimated
These first experiments demonstrate viability of technique
OCT vs. QOCT
After Nasr, Goode, Nguyen, Rong, Yang, Reinhard, Saleh, and Teich, “Quantum Optical Coherence Tomography of a Biological Sample,” Opt. Commun. 282, 1154 (2009).
PBS
PBS
NPBS
QWP
xyBiological Sample
NLC
D1
D2
Cx,y(z)
z
QWP
LPF
LPF
z
x406 nm
Kr+ -
ion
Lase
r
1.25-cm-thick antireflection-coated glass slab
QOCT of Onion-Skin Cells in 3D (Experiment)
A-Scan
0.80
0.85
0.90
0.95
1.00
Nor
mal
ized
Coi
ncid
ence
Rat
e
z (μm)–10 0 10 20
7.5 μm
After Nasr, Goode, Nguyen, Rong, Yang, Reinhard, Saleh, and Teich, “Quantum Optical Coherence Tomography of a Biological Sample,” Opt. Commun. 282, 1154 (2009).
3D Contours of Constant Coincidence Rate
−40
20
−20
40
00−10
10−20
20
xy
z
0
C-Scan(xy)
B-Scan(xz)
Position (μm)
Posit
ion
(μm
)
Position(μm)
C = 0.90
Sample coated with BSA-functionalized gold nanoparticles
B-Sc
an(y
z)
After Nasr, Goode, Nguyen, Rong, Yang, Reinhard, Saleh, and Teich, “Quantum Optical Coherence Tomography of a Biological Sample,” Opt. Commun. 282, 1154 (2009).
75 µm
x
y
z
1.00
0.85
0.95
0.90
Nor
mal
ized
Coi
ncid
ence
Rat
e
Transverse resolution
12 µm
xy
z
30 µm
100 µm
C-Scans
1 µm 2 µm0 µm−1 µm
z = −5 µm −3 µm −2 µm−4 µm
3 µm 4 µm 5 µm 6 µm
100 µm
75 µmx
y
z
1.00
0.85
0.95
0.90
Nor
mal
ized
Coi
ncid
ence
Rat
e
C-Scans
After Nasr, Goode, Nguyen, Rong, Yang, Reinhard, Saleh, and Teich, “Quantum Optical Coherence Tomography of a Biological Sample,” Opt. Commun. 282, 1154 (2009).
x
z
1.00
0.85
0.95
0.90
y
75 µm
xy
z
30 µm
100 µm
B-Scans
Nor
mal
ized
Coi
ncid
ence
Rat
e
Transverse resolution
12 µm
Applications of OCT and QOCTApplications of OCT and QOCT•• Transparent tissue: Transparent tissue: eye: retinal nerve fiber layer, retinal thickness, eye: retinal nerve fiber layer, retinal thickness, contour changes in the optic disk; subcutaneous blood vesselscontour changes in the optic disk; subcutaneous blood vessels
•• Turbid media: Turbid media: vascular wall, vascular wall, placquesplacques
•• PolarizationPolarization--OCT: OCT: tissues with collagen or tissues with collagen or elastinelastin fibers: muscle, fibers: muscle, tendons; normal and thermally damaged soft tissuestendons; normal and thermally damaged soft tissues
Continuing Challenges for QOCTContinuing Challenges for QOCTLimited photon flux: improvement via decreased entanglement timeLimited photon flux: improvement via decreased entanglement timeLimited axial resolution: improvement via Limited axial resolution: improvement via increased source bandwidthincreased source bandwidth
Recent Improvements Enabling Biological QOCTRecent Improvements Enabling Biological QOCT• Compact optical configurationCompact optical configuration•• Use of lenses to enhance spatial resolution Use of lenses to enhance spatial resolution •• Use of PBS/Use of PBS/QWPsQWPs to increase photon flux (factor of 4)to increase photon flux (factor of 4)•• Enhanced sample preparation using gold Enhanced sample preparation using gold nanoparticlesnanoparticles and BSAand BSA
Biological QOCT: SummaryBiological QOCT: SummaryFirst demonstration of the interaction of a quantum-entangled entity and a biological system (nonplanar, scattering, diffusive medium) — entanglement survived the interaction to create an imageDemonstration of the viability of quantum 3D imaging of a biological sample Gold nanoparticles were used to enhance the sample reflectance — a new paradigm for quantum imagingAxial resolution (7.5 μm) can be improved to 1μm. Transverse resolution (12 μm) can be improvedScan time remains too long (but pump power was only 2 mW, corresponding to 0.5 pW of downconverted photons or 106 photon pairs/sec)
Further AdvancesFurther AdvancesQuasi-phase matched (QPM) downconversion (increased photon flux)Chirped quasi-phase-matched downconversion (increased bandwidth)QOCT resolution enhancement via chirped-QPM downconversionQOCT resolution enhancement via superconducting single-photon detectorsPhoton-counting OCT (biological) at λ = 1 μm using chirped-QPM SPDCQuantum-mimetic implementations of QOCTEntangled-photon generation via guided-wave parametric downconversionUse of ultrafast compression techniques for generic quantum imaging
Quasi-Phase-Matched (QPM) Downconversion
Signalωs = ωp /2 + Ω
y
Pump ωp
Idler ωi = ωp /2 _ Ω
Periodically-PoledNonlinear Crystal
Increased Photon Flux
ChirpedChirpedQuasi-Phase-Matched
(QPM) Downconversion
Increased Spectral Bandwidth
QOCT with ChirpedQOCT with Chirped--QPM Downconversion QPM Downconversion Enhances ResolutionEnhances Resolution
After Carrasco, Torres, Torner, Sergienko, Saleh, and Teich, “Enhancing the Axial Resolution of Quantum Optical Coherence Tomography by Chirped Quasi-Phase-Matching,”
Opt. Lett. 29, 2429 (2004)
Chirp parameter
1 μ m
After Nasr, Carrasco, Saleh, Sergienko, Teich, Torres, Torner, Hum, and Fejer, “UltrabroadbandBiphotons Generated via Chirped Quasi-Phase-Matched Optical Parametric Down-Conversion,”
Phys. Rev. Lett. 100, 183601 (2008)
Enhancement of QOCT Resolution Enhancement of QOCT Resolution via Chirped QPM: 19 via Chirped QPM: 19 μμm to 1 m to 1 μμmm
Enhancement of QOCT Resolution via Enhancement of QOCT Resolution via Increase in Detector BandwidthIncrease in Detector Bandwidth
After Nasr, Minaeva, Goltsman, Sergienko, Saleh, and Teich, “Submicron Axial Resolution in an Ultrabroadband Two-Photon Interferometer Using Superconducting Single-Photon Detectors,”
Opt. Express 16, 15104 (2008)
Quantum-MimeticsPhase-Sensitive Optical Coherence Tomography
After B. I. Erkmen and J. H. Shapiro, “Phase-Conjugate Optical Coherence Tomography,” Phys. Rev. A 74, 041601 (2006)
J. de Boer et al., IEEE J. Select. Top. Quantum Electron. 5, 1200-1204 (1999)
Shuliang Jiao and Lihong Wang, OE Magazine, pp. 20- 22 (July 2003)
• TISSUES WITH COLLAGEN OR ELASTIN FIBERS, E.G. MUSCLE, TENDONS
• NORMAL AND THERMALLY DAMAGED SOFT TISSUE
OCT
PS-OCT
Polarization-Sensitive OCT
Properties of TypeProperties of Type--I and TypeI and Type--II Entangled PhotonsII Entangled Photons(a) TYPE-I SPDC
(b) TYPE-II SPDC
PUMP BEAM
NONLINEARCRYSTAL
PUMP BEAM
NONLINEARCRYSTAL
momentum: kp = ks + ki
energy: ωp = ωs + ωi
PHASE MATCHING
TYPE‐IISPDC
COINCIDENCEDETECTION
PULSED PUMPLASER
D1
D2
PBS
NPBS
HR 400 LP 695
PUMPREMOVAL
MIRROR
PBS
BEAMSPLITTER
D1
HWP Q
Q
LINEAR ROTATORGIVESOR
SAMPLEELLIPTICAL
REFERENCE ARM
SAMPLE ARM
R (τ )
NLC
Polarization-Sensitive QOCT: Theory
After Booth, Di Giuseppe, Saleh, Sergienko, and Teich, “Polarization-Sensitive Quantum-Optical Coherence Tomography,” Phys. Rev. A 69, 043815 (2004)
10.40 10.44 10.48 10.52 10.56 10.600
40
80
120
160
200
CO
INC
IDEN
CES
/ 5
SEC
ON
DS
NANOMOVER POSITION (mm)10.44 10.48 10.52 10.56 10.60
0
40
80
120
160
200
240
280
320
CO
INC
IDEN
CES
/ 20
SEC
ON
DS
NANOMOVER POSITION (mm)
(a) NO ZINC SELENIDE (b) 6‐mm ZINC SELENIDE
30 μm30 μm
Polarization-Sensitive QOCT: Experiment
After Booth, Saleh, and Teich, “Polarization-Sensitive Quantum-Optical Coherence Tomography: Experiment,” Opt. Commun. 284, 2542 (2011)
CoCo--propagating SPDC in waveguidespropagating SPDC in waveguides
ωp ωs ωi
ωi ωsDirection Waveguide modes
345
11 22
Δβ1 = β p(mp ) − β s
(0 ) − β i(1)
Δβ 2 = β p(mp ) − β s
(1) − β i(0 )
Phase mis-matching
Δβ1 ≠ Δβ2In general,by controlling waveguide dimensions
Δβ1 = Δβ2Λ1 = Λ 2
Single polingperiod
Modal Entanglement
Modal, Spectral, and Polarization Entanglement in Guided-Wave Parametric Downconversion
After Saleh, Saleh, and Teich, “Modal, Spectral, and Polarization Entanglement in Guided-Wave Parametric Down-Conversion,” Phys. Rev. A 79, 053842 (2009)
Example: Modal entanglement of nondegenerate photons via frequency separation
After Saleh, Di Giuseppe, Saleh, and Teich, “Photonic circuits for generating modal, spectral, and polarization entanglement,” IEEE Photonics Journal 2, 736 (2010)
Modal, Spectral, and Polarization Entanglement in Photonic Circuits
-0.5 0.0 0.50
2000
4000
6000
0.0
0.5
1.0 (a)
φ (Ω
) (ra
d)
NO
RM
AL
IZE
D |
φ (Ω
) |
-1000 -500 0 500 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4(c) HOM
SFG
NO
RM
AL
IZE
D S
IGN
AL
TEMPORAL DELAY τ (fsec)
(b)
NORMALIZED FREQUENCY Ω / ω0
-0.5 0.0 0.50
2000
4000
6000
0.0
0.5
1.0 (a)
φ (Ω
) (r
ad)
NO
RM
ALI
ZED
| φ
(Ω) |
-1000 -500 0 500 10000.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4(c) HOM
SFG
NO
RM
ALI
ZED
SIG
NA
L
TEMPORAL DELAY τ (fsec)
(b)
NORMALIZED FREQUENCY Ω / ω0
Biphoton Compression Can Make Entangled-Photon Photoemission, Microscopy,
and Lithography Work
After Nasr, Carrasco, Saleh, Sergienko, Teich, Torres, Torner, Hum, and Fejer, “UltrabroadbandBiphotons Generated via Chirped Quasi-Phase-Matched Optical Parametric Down-Conversion,”
Phys. Rev. Lett. 100, 183601 (2008)
Boston University:Boston University:•• AymanAyman AbouraddyAbouraddy•• Mark BoothMark Booth•• Francesco Francesco LissandrinLissandrin•• NishantNishant MohanMohan•• Olga Olga MinaevaMinaeva•• Julie Julie PrainoPraino•• Mohammed SalehMohammed Saleh•• David SimonDavid Simon•• Jason StewartJason Stewart•• Andrew WhitingAndrew Whiting•• Tim Tim YarnallYarnall
•• Giovanni Di GiuseppeGiovanni Di Giuseppe•• Martin Martin JaspanJaspan•• BoshraBoshra NasrNasr
University of MarylandUniversity of Maryland--College ParkCollege Park::•• John John FourkasFourkas•• Rick Rick FarrerFarrer•• Chris Chris LaFrattaLaFratta
InstitutInstitut de de CiCièènciesncies FotòniquesFotòniques::•• Silvia CarrascoSilvia Carrasco•• Juan TorresJuan Torres•• LluisLluis TornerTorner
Stanford University:Stanford University:•• David HumDavid Hum•• Martin Martin FejerFejer
ACKNOWLEDGMENTS
Army Research Office
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