nonlinear optics: past successes and future challenges · 2017. 11. 20. · optical phase...
TRANSCRIPT
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Nonlinear Optics: Past Successes and Future Challenges
Presented at the Conference on Lasers and Electro-Optics and Quantum Electronics andLaser Science Conference (CLEO: 2012), 6-11 May 2012 in San Jose, California.
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Making Ottawa the world’s photonics center
OTTAWA, Ontario, Canada –
A $55 million photonics center that was expected to break ground on the
make Ottawa the global hub of photonics.
From Photonics Spectra Magazine
Our research interests include Nanophotonics Plasmonics Photonic crystals Photonic device Applications of slow and fast light Quantum nonlinear optics Optical methods for quantum information
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Why Study Nonlinear Optics?
It is good fundamental physics.
It leads to important applications.
It is a lot of fun.
Demonstrate these features with examples in remainder of talk.
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Nonlinear Optics and Light-by-Light Scattering
The elementary process of light-by-light scattering has never been observed in vacuum, but is readily observed using the nonlinear response of material systems.
Nonlinear material is fluorescein-doped boric acid glass (FBAG)
M. A. Kramer, W. R. Tompkin, and R. W. Boyd, Phys. Rev. A, 34, 2026, 1986.W. R. Tompkin, M. S. Malcuit, and R. W. Boyd, Applied Optics 29, 3921, 1990.
n2�)%$*��Ⱦ���14 n2(silica) [But very slow response!]
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Brief Introduction to Nonlinear Optics
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Timeline – The Early Days of Nonlinear Optics
1958 - Schawlow and Townes; optical maser (laser) proposed
1960 - Maiman, ruby laser demonstrated
1961 - Franken, Hill, Peters, and Weinreich, second-harmonic generation (SHG) observed
1962 - Armstrong, Bloembergen, Ducing, and Pershan; systematic formulation of NLO
1962 - McClung, Hellwarth, Woodbury, and Ng, stimulated Raman scattering (SRS)
1964 - Chiao, Garmire, and Townes, self-trapping of light
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$1 online
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Some Fundamental Nonlinear Optical Processes: II
Sum-Frequency Generation
r (2)
t1
t 2
t1
t 2
t3
t3 = t1 +t2
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rt
tt = t < t
Optical Parametric Amplification
Optical Parametric Oscillator (very broadly tunable)
tt
t
Difference-Frequency Generation and Optical Parametric Amplification
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Nonlinearcrystal | (2)
IdlerSignal
PumpAmpli!ed
signalSignal
bandwidth
a k P
k I" ,k S" ,
Optical Parametric Amplication Can Amplify Extremely Broadband Pulses
tt
t
Work of Jake Bromage and others at U. Rochester LLE.See also Lozhkarev et al. Laser Phys. Lett. 4, 421 (2007) and Y. Tang et al. Opt. Lett. 33, 2386 (2008).
Goal: Design laser source capable of reaching focused intensities as large as 1024 W/cm2.
Can amplify extremely short laser pulses or broadband chirped pulses.
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Parametric Downconversion: A Source of Entangled Photons
The signal and idler photons are entangled in:
(a) polarization
(b) time and enegy
(c) position and transverse momentum
(d) angular position and orbital angular momentum
tp
ts
ti
kp
ks ki
Entanglement is important for:
(a) Fundamental tests of QM (e.g., nonlocality)
(a) Quantum technologies (e.g., secure communications)
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Nonlinear Optics Leads to Creation of Entangled Photons
Quantum Correlations in Optical Angle-Orbital Angular Momentum Variables, Leach et al., Science 329, 662 (2010).
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Optical Phase Conjugation: A Nonlinear Optics Success Story
Zakharenkov, Clatterbuck, Shkunov, Betin, Filgas, Ostby, Strohkendl, Rockwell, and Baltimore, IEEE JSTQE (2007).
distortingmedium
phase-conjugate mirror
���$�SKDVH�FRQMXJDWH�PLUURU��D�QRQOLQHDU�RSWLFDO�GHYLFH��FDQ�UHPRYH�WKH�LQIOXHQFH�RI� aberrations in double pass.
���3KDVH�FRQMXJDWLRQ�LV�H[WUHPHO\�XVHIXO�LQ�KLJK�SRZHU�ODVHU�V\VWHPV��N:�DYHUDJH�SRZHU�SKDVH�FRQMXJDWH�PDVWHU�RVFLOODWRU�SRZHU�DPSOLILHU
QHDU�GLIIUDFWLRQ�OLPLWHG�RXWSXW
(Zeldovich, Pilipetsky, Shkunov, Yariv, Hellwarth, Fisher, 1980s).
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Intense Field and Attosecond Physics
Attosecond pulses to sample a visible E-field
atomic core
High-harmonic generation Measuring the molecular nitrogen wavefunction
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Theory of nonlinear optics
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Local Field E!ects in Nonlinear Optics
Bloembergen (1962, 1965) showed that E PEloc
!(3)(" = " + " ! ") = N#(3)|L(")|2[L(")]2.
where #(3) is the second hyperpolarizability and where
L(") =$(") + 2
3
For the typical value n = 2, L = 2, and L4 = 16. Local field e!ectscan be very large in nonlinear optics! But can we tailor them for ourbenefit?
We have been developing new photonic materials with enhanced NLOresponse by using composite structures that exploit local field e!ects.
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Alternating layers of TiO2 and the conjugated polymer PBZT.
Fischer, Boyd, Gehr, Jenekhe, Osaheni, Sipe, and Weller-Brophy, Phys. Rev. Lett. 74, 1871 (1995).
Measure NL phase shift as a function of angle of incidence.
A composite material can display a larger NL response than its constituents!
Enhanced NLO Response from Layered Composite Materials
3.2 times enhancement!35% enhancement in r(3)
Diode Laser(1.37 um)
polarizer
photodiode
gold electrode
ITO
BaTiO3
1 kHz
lockin amplifier
signal generator
dc voltmeter
glass substrate
AF-30 inpolycarbonate
Quadratic EO effect
Nelson and Boyd, APL 74 2417 (1999)
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Metamaterials and Nanocomposite Materials for Nonlinear Optics
��0D[ZHOO�*DUQHWW ��%UXJJHPDQ���LQWHUGLVSHUVHd)
� Fractal StrXFWXUe ��Layeredh
2a
b
¡i
¡h
¡a¡b
¡a
¡b
- In each case, scale size of inhomoJeneity << optical ZaveleQJWK
-�7KXs all optical properties, VXch as n and Ƶ���, can be described by effective �YROXPH�DYHrDJHG)�YDOXHs
5HFHQW�UHYLHZ��'ROJDOHYD�DQG�%R\G��$GYDQFHV�LQ�2SWLFV�DQG�3KRWRQLFV�����²�����������
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Slow Light, Fast Light, and their Applications
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Controlling the Velocity of Light
– Light can be made to go: slow: vg << c (as much as 106 times slower!) fast: vg > c backwards: vg negative Here vg is the group velocity: vg = c/ng ng = n + Ʒ (dn/dƷ)
Review article: Boyd and Gautier, Science 326, 1074 (2009).
“Slow,” “Fast” and “Backwards” Light
– Velocity controlled by structural or material resonancesabsorption
profile
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n
ng
t
t
t
t 0
absorptionresonance
slow light
fast light
_
n
ng
t
t
t
t 0
gainresonance
g
fast light
slow light
Slow and Fast Light Using Isolated Gain or Absorption Resonances
ng = n + Ʒ (dn/dƷ)
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Light speed reductionto 17 metres per secondin an ultracold atomic gasLene Vestergaard Hau*!, S. E. Harris", Zachary Dutton*!& Cyrus H. Behroozi*§
NATURE | VOL 397 | 18 FEBRUARY 1999 |www.nature.com
1.8 GHz
60 MHz
D line
λ = 589 nm
ω ωc p
|2 = |F =2, M = –2〉 〉F
|1 = |F =1, M = –1〉 〉F
|4 = |F =3, M = –2〉 〉F
|3 = |F =2, M = –2〉 〉F
2
–30 –20 –10 0 10 20 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Tra
nsm
issio
n
a
–30 –20 –10 0 10 20 30
Probe detuning (MHz)
0.994
0.996
0.998
1.000
1.002
1.004
1.006
Refr
active index
b
–2 0 2 4 6 8 10 12
Time (μs)
0
5
10
15
20
25
30
PM
T s
ign
al (m
V)
T = 450 nK
τDelay
= 7.05 ± 0.05 μs
L = 229 ± 3 μm
vg = 32.5 ± 0.5 m s
–1
* Rowland Institute for Science, 100 Edwin H. Land Boulevard, Cambridge,Massachusetts 02142, USA! Department of Physics, § Division of Engineering and Applied Sciences,Harvard University, Cambridge, Massachusetts 02138, USA" Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
Note also related work by Chu, Wong, Welch, Scully, Budker, Ketterle, and many others
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Crucial for many real-world applications
We have identified two preferred methods for producing slow light
(1) Slow light via coherent population oscillations (CPO)
(2) Slow light via stimulated Brillouin scattering (SBS)
Goal: Slow Light in a Room-Temperature
Solid-State Material
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Slow Light by Stimulated Brillouin Scattering (SBS)
1t
L
tS
dI Sdz
= ïgILIS
g = Ƣ2eƷ2
nv c3Ư0ƊB.
z
We often think of SBS as a pure gain process, but it also leads to a change in refractive index
t�� t - 1S L
SBS
gain
refra
ctiv
e in
dex
monochromatic pump laser
Stokes gain
anti-Stokes loss
slow light fast light
Ʒ
Ʒ
TdG
BThe induced time delay is where G= g Ip L and is the Brillouin linewidth B
=
Okawachi, Bigelow, Sharping, Zhu, Schweinsberg, Gauthier, Boyd, and Gaeta Phys. Rev. Lett. 94, 153902 (2005). Related results reported by Song, González Herráez and Thévenaz, Optics Express 13, 83 (2005).
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Slow Light via Coherent Population Oscillations
PRL 90,113903(2003); Science, 301, 200 (2003)
� Ground state population oscillates at beat frequency b (for b < 1/T1).
Kba=
1T
12a
ba=
2T
2
a
bsaturablemedium
t
t + b t + b
E1,
E3,
measureabsorption
� Population oscillations lead to decreased probe absorption (by explicit calculation), even though broadening is homogeneous. � Ultra-slow light (ng > 106) observed in ruby and ultra-fast light (ng = –4 x 105) observed in alexandrite.
� Slow and fast light effects occur at room temperature!
absorptionprofile
Want a narrow feature in absorption profile to give a large dn/dt�
ng = n + t�dn/dt��� 1/T1
1/T2
T2 << T1
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Relation of CPO to the Basov Mechanism
time delay
propagation distance
leading edge sees far moreabsorption than trailing edge
referencepulse
Assume that Tpulse << T1 = time scale for saturation changes
Then absorption decreases with time during pulse due to saturation
T(response)
CPO slow light: a strong pump beam createsa narrow transparency window, and strong spectral variation of the refractive index leads to a large group index.
Basov mechanism: an isolated intense pulse passing through a saturable material experiences a time delay.
�
�
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Slow and Fast Light in an Erbium Doped Fiber Amplifier
6 ms
outin
• Fiber geometry allows long propagation length• Saturable gain or loss possible depending on pump intensity
-0.1
-0.05
0
0.05
0.1
0.15
Frac
tiona
l Adv
ance
men
t
10 100Modulation Frequency (Hz)
10 3 10 4 10 5
- 97.5 mW- 49.0 mW- 24.5 mW- 9.0 mW- 6.0 mW- 0 mW
Advance = 0.32 ms
InputOutput
Time
FWHM = 1.8 ms
Schweinsberg, Lepeshkin, Bigelow, Boyd, and Jarabo, Europhysics Letters, 73, 218 (2006).
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Topic 1: Photon Drag Effects with Slow Light
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For L = 25 mm, v = 2000 cm/s, displacement = 6 nm.
Transverse Photon Drag
Measured by R.V. Jones, 1972.
L
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Observation of Rotary Photon Drag
Franke-Arnold, Gibson, Boyd and Padget, Science, 2011
Effect clearly visible by eye!!
Experimental setup
rotating, 10-cm-long ruby rod
The world as seen through a spinning window.
(Laser-excited ruby has a group index of 106.)
(See also the earlier work of Leach et al., 2008.)
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Topic 2: “Backwards” Propagation and Negative Group Velocities
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Observation of Backward Pulse Propagation in an Erbium-Doped-Fiber Optical Amplifier
0 2 4 6
0
1
2
3
time (ms)
norm
aliz
ed in
tens
ity
in
out
We time-resolve the propagation of the pulse as a function of position along the erbium-doped fiber.Procedure • cutback method • couplers embedded in fiber
1550 nm laser ISO80/20
coupler
980 nm laserWDM
WDM1550980
EDF
Ref
Signal
or
G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, R. W. Boyd, Science 312, 985 2006.
pulse is placed on a cw background to minimizepulse distortion
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Observation of Superluminal and
“Backwards” Pulse Propagation
rcoun erin v
B n rc en
y
Normalized length |ng|Z (m)0 0.5-0.5 1x10-1 5
6t = 0
6t = 3
6t = 6
6t = 9
6t = 12
6t = 15
or or rconc r c
G ring,
c ,
propagation distance
ng negative
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time
puls
e am
plitu
de
road spectral content at points of discontinuityce moves at vacuum speed of light
see, for instance, R. Y. Chiao
Causality?
g g
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Applications of Slow and Fast Light (where the action is now!)
Slow/fast light for interferometeryPhased- and synchronized-array laser radar
Buffers and regenerators for telecom
Construction of quantum memories
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Beam Splitter
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Slow Light Medium
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���The spectral sensitivity of an interferometer is increased by a factor as large as the group index of a material placed within the interferometer.
Slow-light interferometer:
���+Hre is why it works:
Shi, Boyd, Gauthier, and Dudley, Opt. Lett. 32, 915 (2007)6KL��%R\G��&DPDFKR��9XG\DVHWX��DQG��+RZHOO��35/�������������������6KL�DQG�%R\G��-��2SW��6RF��$P��%�����&�������������
���:H�ZDQW�WR�H[SORLW�WKLV�HIIHFW�WR�EXLOG�FKLS�VFDOH�VSHFWURPHWHUV�ZLWK�WKH�VDPH� resoluation as large laboratory spectromters
See also the group of Shahriar on fast-light and interferometry
Simple analysis
Interferometry and Slow Light
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Slow-down factors of greater than 100 have been observed in such structures.
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Regeneration of Pulse Timing
time window
Need to recenter each pulse in its time window
Removes timing jitter caused by NL and
environment effects in fiber
Most conveniently done by access to both slow
and fast light
Need only approximately ±1 pulse width of delay!
Z. Shi, A. Schweinsberg, J. E. Vornehm Jr., A. Martinez Gamez, and R. W. Boyd, Physics Letters A 374 4071–4074 (2010).
Recent implementation using SBS with EO-contolled gain spectrum
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Phased-Array Laser Radar Based on Slow Light
Schweinsberg et al., Optics Express 19, 15760 (2011)Schweinsberg et al., Optics Letters, 37 329 (2012).
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Nonlinear Optics and Quantum Information Science
���:H�use nonlinear optics to create quantum states of light
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How many bits of information can one photon carry?
Can we perform quantum communications with more thanone bit of classical information per photon?
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BucketDetector
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Basis 1 (LGs) Basis 2 (Angular)Basis 1 (LGs)Theory Experiment Experiment Theory
Quantum Key Distribution with Many Bits Per PhotonOffers absolutely secure communicationsEncode in a large alphabet (the Laguerre-Gauss modes)
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Thank you for your attention!
NLO is as exciting today as it was 51 years ago NLO has spun off many new research fields, such as ultrafast phenomena, photonics, optical solitons, . . . One exciting future direction is that of quantum nonlinear optics
Closing Remarks