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									                                                                                                                   CPCC
                        Invited paper at the       14th
                                              Coherent Laser Radar Conference
                                       Snowmass, 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: (847) 491-4128; Fax: (847) 467-5319
                                         E-mail: kumarp@northwestern.edu

                                         2Department of Electrical Engineering
                             University 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)

Center for Photonic Communication and Computing           7/10/2007 Slide 1   McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                                                  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



Center for Photonic Communication and Computing    7/10/2007 Slide 2   McCormick School of Engineering and Applied Science
                                                                                                                   CPCC

                                      Quantum Laser Radar


                              Velocity v                                      Classical
                               for SAR                                       or Quantum
                                                                                                            Target
                                                                                                        Glint / Speckle

                                            Optical              Transmit
                     Transmitter
                                        Pre-processing            Optics

                                                  Coherent                               Atmospheric
                                                  Processing                             Turbulence
                                           Optical               Receive
                      Receiver
                                       Post-processing            Optics




                                                                       Quantum return severely
                     Direct                 PIA                           degraded by loss
                   Heterodyne               PSA                          keep quantum local
                   Homodyne                 (2)
                                            (3)
                                                    PIA = Phase Insensitive Amplifier
                                                    PSA = Phase Sensitive Amplifier
Center for Photonic Communication and Computing          7/10/2007 Slide 3    McCormick School of Engineering and Applied Science
                                                                                                                      CPCC
                                  Quantum Mechanics of Linear
                                       Optical Amplifiers
    Lumped Amplifier Model:                           Haus & Mullen, 1962; Caves, 1982; Yuen, 1992

                                                                      • For PIA:
                                                                      • For PSA:              ˆ  G a  
                                                                                              b     ˆ ˆ
               ˆ
               a                                  ˆ
                                                  b
                              G                                       •
                                                                                  ˆ  Gˆ G  1 a (G  1)
                                                                            e.g., b
                                                                                  EDFA: ˆaˆ   N2
                                                                                                   ˆ
                                           ˆ ˆ                                                          N 2  N1
      [ a, a ]  1
        ˆ ˆ                                [b, b  ]  1
                                                                      • Or in terms of quadratures
                                                                      • Quantum mechanics demands that
                                                                             ˆˆ ˆ
                                                                                b G  1 at the i
                                                                                                     1
                                                                                      ga    ˆ  very least
                                                                                                1       ˆ
                                                                                                        a         2
    • Phase Insensitive Amplifiers                                                                         g
      (PIA)
                                                                      • Ideal amplifier can benoise source
                                                                        No need for an extra modeled with
           –   Erbium-doped fiber amplifier
           –   Semiconductor optical amplifier
                                                                            ˆ
                                                                              G 1 v
                                                                                     ˆ          and      v  0
                                                                                                         ˆ
           –   Fiber Raman Amplifier                                  • For homodyne detection (and for
           –   Optical parametric amplifier                             For homodyne with N a  )
                                                                      • direct detectiondetection (and1for
    • Phase Sensitive Amplifiers                                            direct detection with N a  1 )
                                                                          NFPSA  1 (0 dB)
      (PSA)                                                                      G  1 G  1
           – Optical parametric amplifier                            NFPIA  1        3 dB
                                                                                  G
Center for Photonic Communication and Computing         7/10/2007 Slide 4        McCormick School of Engineering and Applied Science
                                                                                                               CPCC
                                Pictorial View of Amplification of
                                      Coherent Input Light


        E=X+iY                                                        Y

                       Y                                 Phase-
                                                      insensitive

                                                                                        sout2 = (2G -1) sin2

                                                                                                                 X
                                          X
                                                                      Y                          sX2 = g sin2
                                                                                                 sY2 = g-1 sin2

                                                          Phase-
                                                         sensitive
                 t




       E = X cos w t - Y sin w t                                                                                  X

Center for Photonic Communication and Computing   7/10/2007 Slide 5       McCormick School of Engineering and Applied Science
                                                                                                              CPCC

                          Quantum-Limited Sensitivity of Imaging

                 Amplitude Objects:                                           Phase Objects:


                             q




                                                                                               q



          Spatially white shot noise          1
                                             | |2




             • M. I. Kolobov and P. Kumar, “Sub-shot–noise 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).


Center for Photonic Communication and Computing      7/10/2007 Slide 6   McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                                                  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



Center for Photonic Communication and Computing    7/10/2007 Slide 7   McCormick School of Engineering and Applied Science
                                                                                                                     CPCC

                                      Quantum Imaging LADAR


             A quantum enhancement of its classical counter-part
                – the JIGSAW LADAR.


                                                  Quantum Image               Detector
                                                    Enhancer                   Array
                                                                                                  Quantum Image       Detecto
                                       Receiving                                                     Enhancer           Array
            Target                      Optics                                         R. M. Marino and W. R. Davis, Jr.,
                                                2w                                      “Jigsaw: a foliage-penetrating 3D
                                                                                         Receiving
                                            w Transmitter
                                                       Target                                imaging laser radar system,”
                                                                                           Optics
  (a)
                                                                                             Lincoln Lab. J. 15, 23 (2005)
                                                                                                   2w
                                                   (a)                                       w Transmitter
                      Squeezed
                       vacuum                                     Pump
                                   Spatially
  (b)                                                                 Squeezed
                                  broadband                     Amplified
                                                                       vacuum                                   Pump
                 Input Image
             Quantum signal Enhancer PSA                                                     Spatially
                                        (b)                        signal
           PSA – phase-sensitive amplifier
                     Pump                                                                   broadband         Amplified
                                                                        Input signal
              (“squeezer / anti-squeezer”)                                  Pump
                                                                                               PSA             signal
                     (b)
                                                                        (b)
Center for Photonic Communication and Computing          7/10/2007 Slide 8      McCormick School of Engineering and Applied Science
                                                                                                            CPCC
                           Fundamental Factors Contributing to
                               Degradation of Resolution

    a) Cutting off of high-spatial-frequency components by finite aperture size is equivalent
       to using a beamsplitter adding vacuum fluctuations at these frequencies.

    b) In addition, the signal-to-noise ratio of all spatial-frequency components is further
       degraded by quantum efficiency  of the photodetector in image plane.



         Spatial-frequency (lens) plane           Spatial-frequency (lens) plane            Image (focal) plane


                                                          [Squeezed]
                                                            vacuum

                                                                          N/ incident Loss N photons
                                                             Signal
                                                                            photons    (1–) received
                Signal    [Squeezed]
                            vacuum
                                                          [Squeezed]
                                                            vacuum
       (a)      Finite aperture                   (b)                                              Ideal detectors




Center for Photonic Communication and Computing   7/10/2007 Slide 9    McCormick School of Engineering and Applied Science
                                                                                                            CPCC
                                          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
                          /(D SNR ) =  /( D N ) ,
           since the classical coherent-state SNR is given by the # of
           detected photons N.


Center for Photonic Communication and Computing   7/10/2007 Slide 10   McCormick School of Engineering and Applied Science
                                                                                                            CPCC
                          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
                                                     1 T 1
                                                  1        ,
                                                      T S
          which can be made arbitrarily close to unity by using squeezing factor S >> 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 >100, 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.


Center for Photonic Communication and Computing   7/10/2007 Slide 11   McCormick School of Engineering and Applied Science
                                                                                                               CPCC
                              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 >> 1. Thus, if without QIE the detected number of photons is N and the
        resolution is
                                                    /( D N ) ,
         the QIE-enhanced resolution estimate becomes:


                                                    /( D N ) .

Center for Photonic Communication and Computing      7/10/2007 Slide 12   McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                                                  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



Center for Photonic Communication and Computing   7/10/2007 Slide 13   McCormick School of Engineering and Applied Science
                                                                                                                                   CPCC

                                  Parametric Image Amplification

                       Pulsed Nd:YAG Laser
                               Pump
                                                                             Illustration of broad spatial bandwidth
                              (532 nm)
                                         Ps HWP                                  of an optical parametric amplifier
                                                        Signal
      Filter   KTP                                                    (b)
                                                        Input

                                                                            kp       kp                                               ks
                        DBS                         (1064 nm)
                                                                                                  (2) Crystal 
                                                                                                                        
               (OPA)                     Object                                                   KTP KTP 

                                                  CCD                       ks       ks                                               ki
         Fourier Plane                                                                                (OPA) (OPA)
                                         Image Plane
                   CCD
                                                                      keff  0 for          ks        ks          ki         ki
                                                                      q  qmax  k p / length         q        q              keff keff
         M. L. Marable, S-K. Choi, and P. Kumar,
             Optics Express 2, 84–92 (1998).
                                                                                                          kp       kp
                          Pump                                    bare           amplified
                                      16 lines/mm                                             idler
                                                                 signal           signal


               Object Plane                                                                                    Image Plane


                                                                                 Gavrielides, et al., J. Appl. Phys. 62, 2640 (1987)
Center for Photonic Communication and Computing         7/10/2007 Slide 14          McCormick School of Engineering and Applied Science
                                                                                                             CPCC

                                Parametrically Amplified Images

      Object Plane                          Image Plane                                  Fourier Plane
                                      bare amplified
        16 lines/mm                                  idler
                                     signal signal
                                                                          Bare
                                                                         Signal

                                                                                        -16       0      +16      mm-1


                                                            Amplified Signal
       USAF Test Pattern                                    (Low-Pass OPA)



                                                            Amplified Signal
                                                           (Band-Pass OPA)

                                                                                                       signal
                                                                     Correlated
                                                                    Twin Beams
                                                                                        idler


Center for Photonic Communication and Computing    7/10/2007 Slide 15   McCormick School of Engineering and Applied Science
                                                                                                                                                              CPCC

                                                    Noise-Free Image Amplification

                            Intensity Profile                                   Noise Power Profile                   Pulsed Nd:YAG Laser
                 1000                                                  40
                 800
                                                                       30




                                                        (arb. units)
  (arb. units)




                 600                                                                                                                                            Signal
                                                                       20                                               PZT
                 400                                                                                                                                            Input
                                                                       10
                 200
                                                                                                                                        P HWP                   1064 nm
                   0                                                    0
                        0   1      2     3      4   5                       0     1       2     3     4     5
                                                                                                                      Pump       532 nm     HWP
                             Position (mm)                                            Position (mm)
                                                                                                                                                        P
                                                Y       X                                                             KTP
                                                                                  Filter
                                                                                                                      OPA
                                                Detector                                      HWP QWP                       DBS
                                                                                                                                             Object
                                                                                                                                        (10.1 lines/mm)
                    PSA gain G = 2.5-2.6                               Quantum eff.  = 0.82

                    NFamp+loss  3.25mm KTP                                          5.21mm KTP
                                                                                                                                        1 
                    PSA Exp.   1.05 0.1                                           1.10 0.1                              NF  NFamp 
                     @ peaks    0.2 0.6 dB                                         0.4 0.5 dB                                         G
                    PSA        1.1                                                 1.1
                    Theory     0.4 dB                                              0.4 dB                             S.-K. Choi, M. Vasilyev, and P. Kumar,
                    PIA        1.7                                                 1.7                                Phys. Rev. Lett. 83, 1938 –1941 (1999).
                    Theory     2.3 dB                                              2.3 dB
Center for Photonic Communication and Computing                                                  7/10/2007 Slide 16      McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                                                  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



Center for Photonic Communication and Computing   7/10/2007 Slide 17   McCormick School of Engineering and Applied Science
                                                                                                                                           CPCC
                                Degenerate-Pump FWM in Fiber
                                        (neglecting dispersion and loss)
                                                  Amplified
 Signal             (3)   Medium (Glass)          Signal                                   1
                                                                                           2E-5
                                                               Depleted                    2E-5
                                                                                           2E-5
                                                                Pump




                                                                             Gain (A.U.)
    Pump               Kerr Nonlinearity                                                   2E-5
                                                    Idler                                  2E-5
                                                                                           1E-5
                                                                                           1E-5
                                                                                           1E-5
                                                                                           8E-6
                                                                                           6E-6
                                                                                           4E-6
                                                                                           2E-6
                                                                                             0
                                                                                            0E0
                                                                                                -20           -10             0        10         20
                                                                                                                        Detuning (nm)
                                                                                                25
                                                                                                          Experimental Data
                                                                                                          Calculated
                                                                                                20        Gain Slope of 203 dB/W/km




                                                                                    Gain (dB)
                                                                                                15

                                                                                                10
                                                                                                                                   p=1539nm
                                                                                                  5                                s =1558nm

                                                                                                  0
                                                                                                      0   2         4     6       8   10    12    14
                                                                                                              Pump Peak Power (W)

                                                                                            Tang et al., Electron. Lett. 39 (2) 195 (2003)
Center for Photonic Communication and Computing         7/10/2007 Slide 18             McCormick School of Engineering and Applied Science
                                                                                                                CPCC

                        Four-Wave-Mixing Process in Optical Fibers

              dPp                                                                      a          p        s
                   αPp  4γ(Pp Ps Pa ) 2 sin θ
                                        1


              dz
              dPs                                                                            0
                   αPs  2γ(Pp Ps Pa ) 2 sin θ
                                 2        1


               dz                                                                 s:   stokes, a: anti-stokes
              dPa                                                                 p:   pump, P: power
                    αPa  2γ(Pp Ps Pa ) 2 sin θ
                                  2        1
                                                                                  :   phase, : loss coefficient
               dz                                                                 :   propagation constant
              dθ                                           1
                   Δβ  γ{ 2Pp  Ps  Pa  [( Pp Ps / Pa ) 2
                                                  2
                                                                                 Δβ  βs  βa  2 β p
               dz
                                            1               1                      =  + 2  Pp,
                       (Pp Pa / Ps ) 2  4(Ps Pa ) 2 ] cos θ} ,
                                 2
                                                                                  g = [( Pp)2 – (/2)2]1/2
                    z  s ( z)  a ( z)  2  p ( z)                         = (Pa(0)/Ps(0))1/2
       Cappellini & Trillo, JOSA B 8, 824 (1991)


                        4 2 Pp 2 2   2  4 Pp cos( )                            Pp sin( )
     G  1  {1                                  2
                                                                      }sinh ( gL) 
                                                                           2
                                                                                                         sinh(2 gL)
                                            4g                                                 g

         Ideally, PSA provides 6 dB more gain than PIA does.
        FOPA-PSA: Gmax ~ {exp(gL)}2,                                  FOPA-PIA: Gmax ~ {exp(gL)}2/4
Center for Photonic Communication and Computing       7/10/2007 Slide 19   McCormick School of Engineering and Applied Science
                                                                                                                           CPCC

                            Experimental Results: Gain Dependence

            Amplification & de-amplification                                          Gain vs. Pump Power




                                                               Signal gain (dB)
                  10                                                          10                        PSA
                  5                                                                                                         5.5 dB
      Gain (dB)




                                                                                  5
                  0

                  -5                                                              0
              -10                                                                                         PIA

                      0        20        40            60                         0        50   100   150   200
                                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
Center for Photonic Communication and Computing   7/10/2007 Slide 20                  McCormick School of Engineering and Applied Science
                                                                                                                                  CPCC

                                          BER Test of the In-Line PS-FOPA

                                   -2         PSA
                              10                                  15
                                                                                            (b)




                                                      Gain (dB)
             Bit-error-rate

                                                                  5
                                                                        60     120 180
                                                                  Power (mW)
                                   -6
                              10                                                    PIA

                                                                                            (c)
                       10
                               -10      (a)
                                   -28               -24          -20
                                              Optical power (dBm)
             Open squares, circles, and diamonds:                                    Stars and pluses:
                 • back-to-back                                                         • back-to-back
                 • 60 km transmission followed by                                       • 60km transmission followed by
                   8 dB gain with PSFOPA                                                  8 dB gain by PIFOPA
                 • 60 km transmission followed by
                   13 dB gain with PSFOPA                                            Tang, Devgan, Grigoryan, & P. Kumar,
                                                                                     IEE Electronics Letters 41, 1072-1074 (2005)
Center for Photonic Communication and Computing                        7/10/2007 Slide 21    McCormick School of Engineering and Applied Science
                                                                                                                                    CPCC

                                          Experimental Setup

                                                              75MHz                      15GHz        40MHz
                                                              ~                          ~      X
                                                                                                       ~

                             EDFA                 PM                                             IM                      1559.8nm




                                         3-stage

                                        FBG
                                                                                                                      PZT

                                     High Power EDFA




                                                                                                              90:10
                                                      Pump isolation
                                                                                                                            HNLF
          Signal Detection             99:1                                       99:1                99:1                    FM



          Gain Monitor for PLL                Ref. Output of PSA                                                      Ref. Input of PSA

Center for Photonic Communication and Computing              7/10/2007 Slide 22            McCormick School of Engineering and Applied Science
                                                                                                                    CPCC
                                                Direct NF Measurement:
                                                  Preliminary Results

                       Pump Isolation

         PSA                                          EXT-75 Detector
                                        50/50




                                                            +/-



                                                          BPF
               ESA               60dB Amp.
                                                       (35-45MHz)




                         1 
           NF  NFamp 
                         G
         NFamp  NF 1
                      0.5 dB (Raman effect)



Center for Photonic Communication and Computing           7/10/2007 Slide 23   McCormick School of Engineering and Applied Science
                                                                                                                 CPCC

                                                  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 (2) crystal and (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.



                                                                      Quantum Image           Detector
                                                                        Enhancer               Array
                                                                                                 Quantum Image         Detecto
                                                                                                      Enhancer          Array
                                                        Receiving                         Receiving
                             Target                      Optics Target                     Optics
                                                                  2w                              2w
                                                            w Transmitter
                                                          (a)                                 w Transmitter
                    (a)

                                                                            Squeezed
                                   Squeezed
               Quantum Image Enhancer                                        vacuum                           Pump
                                                                                               Spatially
             PSA – phase-sensitive amplifier
                                    vacuum                  (b)                   Pump        broadband
                                                                Spatially Input signal                       Amplified
                  (b)
              (“squeezer / anti-squeezer”)                                                       PSA          signal
                                                               broadband Pump   Amplified
                                        Input signal
                                                                  PSA              signal
                                              Pump
Center for Photonic Communication and Computing        7/10/2007 Slide 24   McCormick School of Engineering and Applied Science
                                                                                                            CPCC




                  Thank You for your kind attention.




Center for Photonic Communication and Computing   7/10/2007 Slide 25   McCormick School of Engineering and Applied Science
                                                                                                                       CPCC

                                  Setup for Noise Measurements



                                                                        Idler
                                                                     (-16 mm-1)




                                                    Photodetectors
            Input
                                                                                  KTP
           Signal


       Amplified
         Signal                                                      Signal Output                    Iris           Object
                                                                      (+16 mm-1)

                                                                           Top View of the Layout
             Idler


                                                  Images for Noise
      Amplified                                    Measurements
   Signal / Idler




Center for Photonic Communication and Computing     7/10/2007 Slide 26            McCormick School of Engineering and Applied Science
                                                                                                                                CPCC

                               Spatially Broadband OPA Theory

         Parametric gain: phase-insensitive gain GPIA  
                                                                                         2




                                 phase-sensitive gain                   GPSA  2GPIA  1  2 GPIA (GPIA  1)

                                                               
         Twin beam noise reduction: R    2    2  1  
                                                                                                       ks               ki
                                                                                                              q                 keff

                                                                                                                  kp
                                     i k eff                        i  k eff l
                  [cosh( hl )                sinh( hl )] exp(                  )
                                       2h                                2                    = quantum efficiency

                     ig                 ikeff l                                                   1
                                                                                             h         | g | 2   k eff
                                                                                                                            2
                   sinh( hl ) exp(           )
                     2h                   2                                                        2
                                                                                                
                                                                                             g pump intensity )1/2
                                            q2 1  1
                k eff    k p  k s  ki    (  )
                                            2 k s ki                                   l = length of nonlinear crystal

         ref.: A. Gavrielides, P. Peterson, and D. Cardimona,
               J. Appl. Phys. 62, 2640 (1987).

Center for Photonic Communication and Computing           7/10/2007 Slide 27             McCormick School of Engineering and Applied Science
                                                                                                              CPCC

                               Twin-Beams Noise Reduction



                         vs. OPA Gain                                                 vs. k
                    1                                                   1

                    0                                                   0

                1
                -
                        9/
                         0d
                         .
                         - a
                        = rm
                        k 5 m
                                                                        1
                                                                        -
                                h
                                e
                                Tr
                                 y
                                 o
                2
                -                                                       2
                                                                        -
                                a
                                t
                                a
                                D
                3
                -                                                       3
                                                                        -
                                                                                                            h
                                                                                                            e
                                                                                                            o
                                                                                                            Ty
                                                                                                             r
                4
                -
NoiseRduction(dB)


                                                                        -
                                                                        4                                   a
                                                                                                            t
                                                                                                            a
                                                                                                            D




                                                      NoiseRducton(B)
                5
                -                                                       5
                                                                        -

                6
                -                                                       6
                                                                        -
                 12345678                                                 4-
                                                                          -  2-
                                                                            3- 10 1 2

                               P
                               A
                               Oa
                                i
                                n
                                G                                                     m
                                                                                      (
                                                                                      r
                                                                                      ad
                                                                                       /
                                                                                       m
                                                                                      k )




                    M. L. Marable, S-K. Choi, and P. Kumar, Optics Express 2, 84–92 (1998).



 Center for Photonic Communication and Computing   7/10/2007 Slide 28    McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                                          Amplifier Noise Figure

                                                                                   G
              DC gain vs. 27 MHz gain                 • PIA SNRout =                              SNRin
                                                                           2G  1  2
              4
                                                                                       1   2
                                                               NFamp+loss = 2           
              3                                                                       G G
                                                                                  G
              2                                       • PSA SNRout = G  1   SNRin

                                                                                1
              1                                                 NFamp+loss = 1
                                                                                G
                  1      2        3        4
                                                    PSA gain G = 2.5-2.6           Quantum eff.  = 0.82
        • Experimental NFamp+loss
                                                    NFamp+loss  3.25mm KTP                    5.21mm KTP
               1 (27 MHz gain)
          =                                         PSA Exp.   1.05 0.1                     1.10 0.1
               (DC gain )2                          @ peaks    0.2 0.6 dB                   0.4 0.5 dB
                                                    PSA        1.1                           1.1
        • NFamp+loss = NFamp
                                                    Theory     0.4 dB                        0.4 dB
                      + (1   ) ( G )             PIA        1.7                           1.7
                                                    Theory     2.3 dB                        2.3 dB

Center for Photonic Communication and Computing   7/10/2007 Slide 29   McCormick School of Engineering and Applied Science
                                                                                                                                           CPCC
                                       Telecom-Band High-Gain MFOPA
                                             (Gain Slope ~200 dB/W/km)

         Experimental Setup Tang et al., Electron. Lett. 39 (2) 195 (2003).
                                                                                                            PD                     Scope
                              1.7Gb/s PRBS           EDFA                    MFs
        Pump                                                   FPC          12.5m
                          IM      PM         OBF1
                                                                                               OBF2
                                                                                                                                OSA
           100ns Pulses                                          80:20                                Output
         ~1/30 Duty Cycle               Signal                   Coupler
                                                 Isolator
          p = 1539nm, peak pump power ~12W, s from 1535nm to 1565nm, 0 ~1544 (+/- 3) nm
                         30
                                                                                             25
             Gain (dB)




                                                                                                       Experimental Data
                                                                                                       Calculated
                                                                                             20        Gain Slope of 203 dB/W/km
                         20




                                                                                 Gain (dB)
                                                                                             15
                         10
                                                                                             10

                         1510 1520 1530 1540 1550 1560 1570                                                                   p=1539nm
                                                                                             5                                s =1558nm
                                    Wavelength(nm)
                                                                                             0
        • Gains >20dB over ~30nm using only 12.5m-long MF                                         0    2     4      6       8       10   12   14
                                                                                                           Pump Peak Power (W)
        • A record gain slope of ~203dB/W/Km ( ~8.7

Center for Photonic Communication and Computing             7/10/2007 Slide 30               McCormick School of Engineering and Applied Science
                                                                                                                                  CPCC
                               A Fiber PSA for Double Sideband
                                       Encoded Signals
                                                                                                                 wLO+wD wLO+wD
               Transmission
                   line                             LO                 Data                                           wLO
                                                                                                                    35 GHz
                                      PM                       MZ-IM           CW                                  a p s
                                                                                                           (a)
                                                             Transmitter unit

                                                                                                     -10 (a)
                                            Insertion dB

                            p                                                                       -30
                      a         s
                                                                                                     -50                     Signal
                                                                                         nm
                                                                                                                              path
                                                                                                     -70
                                                                        p                              1559.2 1559.8 1560.4
               Separator                                                                                                p
                                                                                                           (b)
                                      FPC     (a) 1000m                                                            a        s
                                                  HNLF
                             PZT            90/10     ISO FBG                                         20 (b)
                     EDFA    FPC                                                                       0
                         OBF                                          Phase                          -20                      Pump
                                                             (b)   locking unit                      -40                       path
   Tang, Devgan, Voss, Grigoryan, & Kumar, IEEE PTL 17, 1845 (2005)
                                                                                                     -60
                                                                                                        1559.2 1559.8 1560.4
Center for Photonic Communication and Computing                    7/10/2007 Slide 31       McCormick School of Engineering and Applied Science
                                                                                                                              CPCC

                                                 Overall Optical Spectrum

                             0
                                                                     Pump                            SBS
                            -10


                            -20
      optical power (dBm)




                            -30

                                                 Signal                                                 Idler
                            -40


                            -50


                            -60
                                                                   30GHz
                            -70


                            -80
                              1559.2    1559.4            1559.6              1559.8         1560               1560.2           1560.4

                                                                     wavelength (nm)


                             Phase modulation is applied on the total optical beam to suppress
                                             Stimulated Brillouin Scattering.

Center for Photonic Communication and Computing                     7/10/2007 Slide 32   McCormick School of Engineering and Applied Science
                                                                                                            CPCC

                         Limits on Fiber-PSA Noise Figure

                                                                        PSA gain:


                                                                        PSA noise figure:




    Mean # of excess-noise photons:




  Voss, Köprülü, & Kumar, JOSA B 23, 598-610 (2006).
Center for Photonic Communication and Computing   7/10/2007 Slide 33   McCormick School of Engineering and Applied Science

								
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