NoiseFree Amplification: Towards Quantum Laser Radar

1
Invited paper at the 14th Coherent Laser Radar
ConferenceSnowmass, CO July 9, 2007
Noise-Free Amplification Towards Quantum Laser
Radar
Prem Kumar1 Vladimir Grigoryan1 Michael
Vasilyev2 1Center for Photonic Communication and
Computing Northwestern University, Evanston, IL
60208-3118 Tel [phone] Fax (847)
467-5319 E-mail kumarp_at_northwestern.edu 2Depart
ment of Electrical EngineeringUniversity of
Texas at Arlington, Arlington, TX 76019-0016
Work funded by ARO Quantum Imaging MURI and
DARPA through the NRL (Collaboration with Jeffrey
Shapiro of MIT on the MURI)
2
Outline

• Quantum Laser Radar what we mean by it ?
• Quantum Mechanics of Linear Optical Amplifiers
• Noise in phase-insensitive and phase-sensitive
  amplification
• Quantum limited sensitivity of imaging
• Quantum Enhanced Laser Radar
• Quantum enhancement of sensitivity and resolution
• Spatially Broadband Parametric Image
  Amplification
• Quantum correlations in image amplification
• Noise-Free Image Amplification
• Fiber Optical Parametric Amplifiers (FOPAs)
• Phase-insensitive and phase-sensitive FOPAs
• Demonstration of noise-improved digital
  transmission
• Noise-free analog signal amplification
• Summary

3
Quantum Laser Radar
Target Glint / Speckle
4
Quantum Mechanics of Linear Optical Amplifiers
Lumped Amplifier Model
Haus Mullen, 1962 Caves, 1982 Yuen, 1992

• Phase Insensitive Amplifiers (PIA)
• Erbium-doped fiber amplifier
• Semiconductor optical amplifier
• Fiber Raman Amplifier
• Optical parametric amplifier
• Phase Sensitive Amplifiers (PSA)
• Optical parametric amplifier

5
Pictorial View of Amplification of Coherent Input
Light
6
Quantum-Limited Sensitivity of Imaging
Amplitude Objects
Phase Objects
q
q

• M. I. Kolobov and P. Kumar, Sub-shotnoise
  microscopy Imaging of faint phase objects with
  squeezed light, Opt. Lett. 18, 849 (1993).
• P. Kumar and M. I. Kolobov, Four-Wave Mixing as
  a Source for spatially broadband squeezed light,
  Opt. Commun. 104, 374 (1994).

7
Outline

• Quantum Laser Radar what we mean by it ?
• Quantum Mechanics of Linear Optical Amplifiers
• Noise in phase-insensitive and phase-sensitive
  amplification
• Quantum limited sensitivity of imaging
• Quantum Enhanced Laser Radar
• Quantum enhancement of sensitivity and resolution
• Spatially Broadband Parametric Image
  Amplification
• Quantum correlations in image amplification
• Noise-Free Image Amplification
• Fiber Optical Parametric Amplifiers (FOPAs)
• Phase-insensitive and phase-sensitive FOPAs
• Demonstration of noise-improved digital
  transmission
• Noise-free analog signal amplification
• Summary

8
Quantum Imaging LADAR
A quantum enhancement of its classical
counter-part the JIGSAW LADAR.
9
Fundamental Factors Contributing to Degradation
of Resolution

• Cutting off of high-spatial-frequency components
  by finite aperture size is equivalent to using a
  beamsplitter adding vacuum fluctuations at these
  frequencies.
• In addition, the signal-to-noise ratio of all
  spatial-frequency components is further degraded
  by quantum efficiency ? of the photodetector in
  image plane.

10
Quantum Limited Rayleigh Resolution Limit

• Rayleigh resolution limit can be overcome by
  de-convolving the spatial-response function from
  the image data (for soft apertures) or by
  extrapolating signal spectrum into the stop-band
  via analytic continuation (for hard apertures).
• In either case, the SNR of the detected spatial
  frequency components will ultimately determine
  the degree of success of such a procedure, i.e.,
  maximum recoverable resolution of
• ,
• since the classical coherent-state SNR is given
  by the of detected photons N.

11
Improving Resolution Limit by use of
Spatially-Broadband Squeezed Vacuum

• Although information lost by hard-aperturing
  cannot be recovered, the effect of
  soft-aperturing (if it comes from increased
  reflection or scattering losses at high-spatial
  frequencies, or from their deliberate attenuation
  / apodization) can be mitigated
  quantum-mechanically.
• Indeed, if the vacuum input to the equivalent
  beamsplitter is replaced by locally generated
  spatially broadband (i.e., multimode) squeezed
  vacuum with appropriate phase, SNR of the light
  passing through the aperture will remain almost
  unchanged by soft attenuation. More specifically,
  for transmittance T, the SNR will decrease by a
  factor
• which can be made arbitrarily close to unity by
  using squeezing factor S gtgt 1/T.
• For example, to recover the spatial frequency
  content attenuated 100 times by a Lorentzian
  low-pass filter with effective (3 dB) aperture
  size D, we will need S gt100, which will extend
  the effective spatial bandwidth of the filter 10
  times (i.e., produce an effective aperture size
  10D), leading to 10-fold improvement in the
  resolution beyond the classical limit.

12
Quantum Recovery of Information Lost by Detector
Array

• The focal-plane photodetector array has non-unity
  quantum efficiency, ?, whose effect is equivalent
  to adding vacuum noise and degrading the
  signal-to-noise ratio needed for successful
  de-convolution operation.
• While individual p-i-n photodiodes can approach ?
  1, low-received-light requirements of LADAR
  applications demand the use of APD arrays, for
  which ? is limited to 0.2 in the visible
  wavelength range, where silicon APD arrays can be
  fabricated whereas for infrared applications
  (beyond the range of silicon), ? values of the
  detector arrays are significantly (orders of
  magnitude) lower.
• For a PSA gain of G, the improvement of SNR at
  the detector is given by a factor
• G / (G? 1 ?) ? 1/?
• for G gtgt 1. Thus, if without QIE the detected
  number of photons is N and the resolution is
• the QIE-enhanced resolution estimate becomes

13
Outline

• Quantum Laser Radar what we mean by it ?
• Quantum Mechanics of Linear Optical Amplifiers
• Noise in phase-insensitive and phase-sensitive
  amplification
• Quantum limited sensitivity of imaging
• Quantum Enhanced Laser Radar
• Quantum enhancement of sensitivity and resolution
• Spatially Broadband Parametric Image
  Amplification
• Quantum correlations in image amplification
• Noise-Free Image Amplification
• Fiber Optical Parametric Amplifiers (FOPAs)
• Phase-insensitive and phase-sensitive FOPAs
• Demonstration of noise-improved digital
  transmission
• Noise-free analog signal amplification
• Summary

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Parametric Image Amplification
Illustration of broad spatial bandwidth of an
optical parametric amplifier
Gavrielides, et al., J. Appl. Phys. 62, 2640
(1987)
15
Parametrically Amplified Images
Fourier Plane
BareSignal
Amplified Signal (Low-Pass OPA)
USAF Test Pattern
Amplified Signal (Band-Pass OPA)
signal
CorrelatedTwin Beams
idler
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Noise-Free Image Amplification
S.-K. Choi, M. Vasilyev, and P. Kumar, Phys. Rev.
Lett. 83, 1938 1941 (1999).
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Outline

• Quantum Laser Radar what we mean by it ?
• Quantum Mechanics of Linear Optical Amplifiers
• Noise in phase-insensitive and phase-sensitive
  amplification
• Quantum limited sensitivity of imaging
• Quantum Enhanced Laser Radar
• Quantum enhancement of sensitivity and resolution
• Spatially Broadband Parametric Image
  Amplification
• Quantum correlations in image amplification
• Noise-Free Image Amplification
• Fiber Optical Parametric Amplifiers (FOPAs)
• Phase-insensitive and phase-sensitive FOPAs
• Demonstration of noise-improved digital
  transmission
• Noise-free analog signal amplification
• Summary

18
Degenerate-Pump FWM in Fiber(neglecting
dispersion and loss)
Tang et al., Electron. Lett. 39 (2) 195 (2003)
19
Four-Wave-Mixing Process in Optical Fibers
lp
s stokes, a anti-stokes p pump, P
power f phase, a loss coefficient b
propagation constant
k Db 2 k Pp, g (g Pp)2 (k/2)21/2
h (Pa(0)/Ps(0))1/2
Cappellini Trillo, JOSA B 8, 824 (1991)
Ideally, PSA provides 6 dB more gain than PIA
does.
FOPA-PSA Gmax exp(gL)2, FOPA-PIA Gmax
exp(gL)2/4
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Experimental Results Gain Dependence
Gain vs. Pump Power
Amplification de-amplification
10
10
5
Signal gain (dB)
5
Gain (dB)
0
-5
0
-10
50
100
150
200
0
20
40
60
0
Time (ms)
Pump power (mW)
Input signal
measured PSA gain
Output phase scanned
calculated PSA gain
Output phase locked
calculated PIA gain
Output path-matching broken
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BER Test of the In-Line PS-FOPA
PSA
PIA

• Open squares, circles, and diamonds
• back-to-back
• 60 km transmission followed by 8 dB gain with
  PSFOPA
• 60 km transmission followed by 13 dB gain with
  PSFOPA

• Stars and pluses
• back-to-back
• 60km transmission followed by 8 dB gain by PIFOPA

Tang, Devgan, Grigoryan, P. Kumar, IEE
Electronics Letters 41, 1072-1074 (2005)
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Experimental Setup
75MHz
15GHz
40MHz


?

X
EDFA
1559.8nm
IM
PM
3-stage
FBG
High Power EDFA
Pump isolation
HNLF
Signal Detection
Ref. Output of PSA
Ref. Input of PSA
Gain Monitor for PLL
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Direct NF Measurement Preliminary Results
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Summary

• A quantum enhanced version of classical imaging
  LADAR is possible with use of spatially-broadband
  squeezed light and phase-sensitive amplification.
• Noise-free amplification is demonstrated, both in
  c(2) crystal and c(3) fiber media for such
  applications, the latter can be especially useful
  in raster scanned systems.
• Pulsed systems can provide significant optical
  gains and inherent range gating.
• Recent development of carrier-envelope stabilized
  lasers will play a significant role.

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Thank You for your kind attention.
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Setup for Noise Measurements
Top View of the Layout
Images for Noise Measurements
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Spatially Broadband OPA Theory
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Twin-Beams Noise Reduction
vs. OPA Gain
vs. ?k
M. L. Marable, S-K. Choi, and P. Kumar, Optics
Express 2, 8492 (1998).
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Amplifier Noise Figure
DC gain vs. 27 MHz gain

• Experimental NFamploss
  

(27 MHz gain) (DC gain )2
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Telecom-Band High-Gain MFOPA(Gain Slope 200
dB/W/km)
Tang et al., Electron. Lett. 39 (2) 195 (2003).

• lp 1539nm, peak pump power 12W, ls from 1535nm
  to 1565nm, l0 1544 (/- 3) nm

• Gains gt20dB over 30nm using only 12.5m-long MF
• A record gain slope of 203dB/W/Km ( 8.7g)

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A Fiber PSA for Double Sideband Encoded Signals
Separator
Tang, Devgan, Voss, Grigoryan, Kumar, IEEE PTL
17, 1845 (2005)
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Overall Optical Spectrum
Phase modulation is applied on the total optical
beam to suppress Stimulated Brillouin Scattering.
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Limits on Fiber-PSA Noise Figure
Voss, Köprülü, Kumar, JOSA B 23, 598-610 (2006).