## Measurement of quantum-noise correlations in parametric image amplification

Optics Express, Vol. 2, Issue 3, pp. 84-92 (1998)

http://dx.doi.org/10.1364/OE.2.000084

Acrobat PDF (421 KB)

### Abstract

We demonstrate quantum-noise correlations between the spatial frequencies of a parametrically amplified signal image and the generated conjugate (idler) image. Test images were amplified by an optical parametric amplifier that can be operated either as a low-pass or a band-pass amplifier for spatial frequencies. Direct difference detection of the signal and idler spatial frequencies at ±16 mm^{-1} resulted in noise that fell below the shot-noise level by ≃5 dB. Parametric-gain and phase-mismatch dependence of the observed quantum-noise reduction is in good agreement with the theory of a spatially-broadband optical parametric amplifier.

© Optical Society of America

## 1. Introduction

^{1-8}have been reported over the years, there has been little attention devoted to the applications of squeezed light to phenomena in the spatial domain, such as optical imaging, diffraction, and holography. However, it has been proposed that spatially-broadband squeezed light can be used to image faint objects with sensitivity exceeding the shot-noise limit.

^{9,10}In this scheme, the phase object to be imaged is placed in one arm of a Mach-Zehnder interferometer, whose normally-unused input port is illuminated with spatially-broadband squeezed light generated by a traveling-wave optical-parametric amplifier (OPA).

^{11}

*q*be co-generated with a conjugate idler photon at -

*q*. Therefore, to observe quantum correlations in a parametrically-amplified image, we need to sample both the signal and the idler photons at the same magnitude of the spatial frequency.

## 2. Theory

*â*

_{s}and

*â*

_{i}are the input and

*b̂*

_{s}and

*b̂*

_{i}are the output annihilation operators for the signal and idler fields, respectively. In our experiment, there is no idler input field so that 〈

*â*

_{i}〉 = 〈

*η*, the expressions for the parametric gain and the quantum-noise reduction in the case of a collinear twin-beams experiment

^{25}can be written as

*g*and

*R*have the same forms as in the collinear case, but the coupling coefficients

*μ*and

*ν*are given by

^{26}

*z*,

*κ*is the parametric-gain coefficient which is proportional to the intensity of the pump beam, and

*ℓ*is the length of the χ

^{(2)}-nonlinear medium—a 5.21-mm long KTP crystal in our experiment. Optimum amplification occurs when Δ

*k*

_{eff}= 0. At the spatial frequency of

*q*= 0, this phase matching condition is fulfilled for Δ

*k*=

*k*

_{p}-

*k*

_{s}-

*k*

_{i}= 0. However, at higher spatial frequencies, phase matching occurs only when Δ

*k*≠ 0. Using the paraxial approximation,

^{26}it can be shown that the effective phase mismatch for a spatial frequency

*q*is given by

*k*become progressively more negative, it is possible to bring increasingly higher spatial frequencies into the phase match condition.

*μ*and

*ν*depend on

*q*through Δ

*k*

_{eff}, we can evaluate the signal and idler outputs, and the quantum-noise reduction, as a function of the spatial frequency for any given signal input. The simplest case is for an input signal with a small spread centered at

*q*= 0, as shown in Fig. 1(a). We define

*ξ*=

*q*/2

*π*so that the spatial frequency

*ξ*is in units of mm

^{-1}. Here the phase matching condition is satisfied for Δ

*k*= 0 and we have chosen the OPA gain

*g*≡ |

*μ*(0)|

^{2}= 4. As expected, the signal and idler outputs as well as the noise reduction are maximized for

*ξ*= 0. From the noise-reduction curve, we estimate that the spatial bandwidth of our OPA is approximately 15mm

^{-1}(HWHM). In this configuration, the OPA functions as a low-pass amplifier for spatial frequencies.

^{-1}. From Fig. 1(a), it is evident that a signal input at +16 mm

^{-1}(or -16 mm

^{-1}) will be amplified very little when Δ

*k*= 0. For this spatial frequency, the phase-matching condition is fulfilled for Δ

*k*= -0.95rad/mm for the parameters of our KTP crystal. In practice, Δ

*k*can be adjusted by rotating the azimuthal angle of the KTP crystal in the OPA so that the incidence angle of the signal changes while that of the pump remains fixed. Note that

*q*remains unchanged in this process since the polar angle is kept fixed. As shown in Fig. 1(b), when Δ

*k*= -0.95rad/mm, the signal at +16 mm

^{-1}is amplified with an OPA gain of

*g*= 4, and the conjugate idler is generated at -16mm

^{-1}. Since the maximum gain and the noise reduction depend on the ability to achieve optimum phase matching for the appropriately chosen Δ

*k*, we can obtain a gain of 4 for the same value of

*κ*as in the low-pass configuration (Δ

*k*= 0). Therefore, the noise reduction at

*ξ*= ±16 mm

^{-1}is not diminished from that at

*ξ*= 0 in the low-pass case, although the spatial-frequency bandwidth is somewhat reduced.

*k*< 0, the OPA acts like a band-pass amplifier, allowing us to amplify higher spatial frequencies more effectively. This feature of optical parametric amplification makes it possible to optimize phase matching, and hence quantum-noise correlations, for a single incident spatial frequency of our choosing. To observe correlations at many different spatial frequencies simultaneously, an OPA with a spatial bandwidth covering all the desired frequencies would be required. Also, a band-pass OPA can be utilized for edge and contrast enhancement in classical parametric amplification of images.

^{16,23}

## 3. Experiments

*p*polarized (parallel to the crystal

*z*-axis) for type II phase-matching in the crystal. The object is placed in the signal-beam path in front of the OPA. A real image of this object is formed in the center of the KTP crystal by a ×1 telescope consisting of two 10-cm focal-length lenses. The spatial frequencies of this image are amplified by the pump beam, which is made coincident with the signal beam using a dichroic beamsplitter. The green pump is blocked after the crystal by using a filter which passes only the IR. CCD cameras are placed in the output image as well as the Fourier planes of a 20-cm focal-length lens that is placed after the filter. The generated idler is orthogonally polarized relative to the amplified signal because of type II phase matching. Therefore, a half-wave plate followed by a polarizing beamsplitter placed after the 20-cm lens allows us to observe either the signal or the idler output in the image as well as the Fourier planes by simply rotating the half-wave plate.

*μ*m (16 lines/mm). The horizontal Fourier transform of this object consists of three main peaks at

*ξ*= 0, ±16 mm

^{-1}with two smaller peaks in between at

*ξ*= ±8mm

^{-1}. As recorded in the output image plane, real images of the bare signal (i.e., with the pump turned off), the amplified signal, and the generated idler are shown in Fig. 3(a) for an OPA gain of ≃1.2. The transverse pattern of the bare signal as recorded in the output Fourier plane is shown in Fig. 3(b). Figure 3(c) shows the transverse pattern of the amplified signal in the output Fourier plane when the OPA was aligned in the low-pass configuration (Δ

*k*= 0) and the pump power adjusted for a gain of ≃4. As shown, the central peak (

*ξ*= 0) was strongly amplified with little amplification occurring at the side peaks (

*ξ*= +16mm

^{-1}). Transverse pattern in the output Fourier plane for band-pass amplification with Δ

*k*= -0.95rad/mm is shown in Fig. 3(d). Here, the pump power was the same as in Fig. 3(c) and the OPA was aligned for maximum amplification of the two side peaks at ±16 mm

^{-1}. These results compare favorably with the theoretical predictions presented in Fig. 1 above.

*and*the Fourier planes. By placing an iris in the Fourier plane that is in front of the OPA (halfway in between the two lenses of the ×1 telescope), we blocked all spatial-frequency components of the input signal pattern except the peak centered at

*ξ*= +16 mm

^{-1}. Thus the input signal had a well defined spatial frequency. The OPA was adjusted for maximum gain at ±16 mm

^{-1}, corresponding to an azimuthal rotation of the KTP crystal of about 0.85° from the angle for phase matching at

*ξ*= 0. In this way the input signal Fourier component was band-pass amplified, and a conjugate Fourier component at

*ξ*= -16mm

^{-1}of the idler beam was generated. Since the amplified signal Fourier component at +16 mm

^{-1}exits the OPA at an angle of 2 × 17 = 34 mrad with respect to the idler Fourier component at -16 mm

^{-1}, it was easy to separate the two with use of plane mirrors. The mirror that sent the beams to the CCD cameras was removed (cf. Fig. 2), and each beam was focused onto a separate photodetector located in the far-field (i.e., in the Fourier plane). Therefore, one detector saw the amplified signal Fourier component at +16 mm

^{-1}, while the other detected the idler component at -16 mm

^{-1}. Twin-beams type of noise measurements were made using direct difference detection, similar to those described in Ref. 25. Noise power of the difference photocurrent was measured at 27 MHz with a 3 MHz resolution bandwidth.

*k*for various values of the OPA gain. Results from one set of data for an OPA gain of ≃3.9 are shown in Fig. 4(b). As pointed out previously, Δ

*k*was varied by rotating the azimuthal angle of the KTP crystal in the OPA. The micrometer readings on the KTP rotation stage were calibrated and converted into units of Δ

*k*for comparison with the theory. As shown, the experimental data are once again in good agreement with the theory (solid curve), once the detection quantum efficiency is taken into account.

## 4. Conclusion

## References

1. | M. Xiao, L.-A. Wu, and H. J. Kimble, “Precision measurement beyond the shot-noise limit,” Phys. Rev. Lett. |

2. | P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, “Squeezed-light-enhanced polarization interferometer,” Phys. Rev. Lett. |

3. | M. Xiao, L.-A. Wu, and H. J. Kimble, “Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit,” Opt. Lett. |

4. | E. S. Polzik, J. Carri, and H. J. Kimble, “Spectroscopy with squeezed light,” Phys. Rev. Lett. |

5. | D. C. Kilper, A. C. Schaefer, J. Erland, and D. G. Steel, “Coherent nonlinear optical spectroscopy using photon-number squeezed light,” Phys. Rev. A |

6. | S. Kasapi, S. Lathi, and Y. Yamamoto, “Amplitude-squeezed, frequency-modulated, tunable, diode-laser-based source for sub-shot-noise FM spectroscopy,” Opt. Lett. |

7. | F. Marin, A. Bramati, V. Jost, and E. Giacobino, “Demonstration of high sensitivity spectroscopy with squeezed semiconductor lasers,” Opt. Commun. |

8. | Y.-Q. Li, P. Lynam, M. Xiao, and P. J. Edwards, “Sub-shot-noise laser Doppler anemometry with amplitude-squeezed light,” Phys. Rev. Lett. |

9. | M. I. Kolobov and P. Kumar, “Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light,” Opt. Lett. |

10. | M. I. Kolobov and I. V. Sokolov, “Multimode squeezing, antibunching in space and noise-free optical images,” Europhys. Lett. |

11. | M. I. Kolobov and I. V. Sokolov, “Spatial behavior of squeezed states of light and quantum noise in optical images,” Sov. Phys. JETP |

12. | P. Kumar, M. L. Marable, and S.-K. Choi, “Quantum properties of the traveling-wave χ |

13. | J. E. Midwinter, “Parametric infrared image converters,” IEEE J. Quantum Electron. |

14. | A. H. Firester, “Parametric image conversion: Part I,” J. Appl. Phys. |

15. | R. A. Andrews, “IR image parametric up-conversion,” IEEE J. Quantum Electron. |

16. | Y. Fainman, E. Klancnik, and S. H. Lee, “Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO |

17. | P. A. Laferriere, C. J. Wetterer, L. P. Schelonka, and M. A. Kramer, “Spatial-frequency selection using downconversion optical parametric amplification,” J. Appl. Phys. |

18. | F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, and T. Laurent, “Picosecond parametric amplification of a monochromatic image,” Nonlinear Opt. |

19. | F. Devaux and E. Lantz, “Parametric amplification of a polychromatic image,” J. Opt. Soc. Am. B |

20. | F. Devaux and E. Lantz, “Ultrahigh-speed imaging by parametric image amplification,” Opt. Commun. |

21. | J. Watson, P. Georges, T. Lépine, B. Alonzi, and A. Brun, “Imaging in diffuse media with ultrafast degenerate optical parametric amplification,” Opt. Lett. |

22. | S. M. Cameron, D. E. Bliss, and M. W. Kimmel, “Gated frequency-resolved optical imaging with an optical parametric amplifier for medical applications,” Proc. SPIE |

23. | E. Lantz and F. Devaux, “Parametric amplification of images,” Quantum Semiclassic. Opt. |

24. | S.-K. Choi, M. L. Marable, and P. Kumar, “Observation of quantum noise correlations in parametric image amplification,” in |

25. | O. Aytür and P. Kumar, “Pulsed twin beams of light,” Phys. Rev. Lett. |

26. | A. Gavrielides, P. Peterson, and D. Cardimona, “Diffractive imaging in three-wave interactions,” J. Appl. Phys. |

**OCIS Codes**

(110.4280) Imaging systems : Noise in imaging systems

(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(270.6570) Quantum optics : Squeezed states

**ToC Category:**

Focus Issue: Experiments on generation and application of quantum light states

**History**

Original Manuscript: November 20, 1997

Published: February 2, 1998

**Citation**

Michael Marable, Sang Kyung Choi, and Prem Kumar, "Measurement of quantum-noise correlations in parametric image amplification," Opt. Express **2**, 84-92 (1998)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-2-3-84

Sort: Journal | Reset

### References

- M. Xiao, L.-A. Wu, H. J. Kimble, "Precision measurement beyond the shot-noise limit," Phys. Rev. Lett. 59, 278-281 (1987). [CrossRef] [PubMed]
- P. Grangier, R. E. Slusher, B. Yurke, A. LaPorta, "Squeezed-light-enhanced polarization interferometer," Phys. Rev. Lett. 59, 2153-2156 (1987). [CrossRef] [PubMed]
- M. Xiao, L.-A. Wu, H. J. Kimble, "Detection of amplitude modulation with squeezed light for sensitivity beyond the shot-noise limit," Opt. Lett. 13, 476-478 (1988). [CrossRef] [PubMed]
- E. S. Polzik, J. Carri, H. J. Kimble, "Spectroscopy with squeezed light," Phys. Rev. Lett. 68, 3020-3023 (1992). [CrossRef] [PubMed]
- D. C. Kilper, A. C. Schaefer, J. Erland, D. G. Steel, "Coherent nonlinear optical spectroscopy using photon-number squeezed light," Phys. Rev. A 54, R1785-R1788 (1996). [CrossRef] [PubMed]
- S. Kasapi, S. Lathi, Y. Yamamoto, "Amplitude-squeezed, frequency-modulated, tunable, diode-laser-based source for sub-shot-noise FM spectroscopy," Opt. Lett. 22, 478-480 (1997). [CrossRef] [PubMed]
- F. Marin, A. Bramati, V. Jost, E. Giacobino, "Demonstration of high sensitivity spectroscopy with squeezed semiconductor lasers," Opt. Commun. 140, 146-157 (1997). [CrossRef]
- Y.-Q. Li, P. Lynam, M. Xiao, P. J. Edwards, "Sub-shot-noise laser Doppler anemometry with amplitude-squeezed light," Phys. Rev. Lett. 78, 3105-3108 (1997). [CrossRef]
- M. I. Kolobov and P. Kumar, "Sub-shot-noise microscopy: imaging of faint phase objects with squeezed light," Opt. Lett. 18, 849-851 (1993). [CrossRef] [PubMed]
- M. I. Kolobov and I. V. Sokolov, "Multimode squeezing, antibunching in space and noise-free optical images," Europhys. Lett. 15, 271-276 (1991). [CrossRef]
- M. I. Kolobov and I. V. Sokolov, "Spatial behavior of squeezed states of light and quantum noise in optical images," Sov. Phys. JETP 69, 1097-1104 (1989).
- P. Kumar, M. L. Marable, and S.-K. Choi, "Quantum properties of the traveling-wave (2) process: theory, experiments, and applications," in Quantum Communication, Computing, and Measurement, O. Hirota, A. S. Holevo, and C. M. Caves, Eds., (Plenum, New York, 1997), pp. 531-544. [CrossRef]
- J. E. Midwinter, "Parametric infrared image converters," IEEE J. Quantum Electron. 4, 716-720 (1968). [CrossRef]
- A. H. Firester, "Parametric image conversion: Part I," J. Appl. Phys. 40, 4842-4849 (1969). [CrossRef]
- R. A. Andrews, "IR image parametric up-conversion," IEEE J. Quantum Electron. 6, 68-80 (1970). [CrossRef]
- Y. Fainman, E. Klancnik, S. H. Lee, "Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3," Opt. Eng. 25, 228-234 (1986).
- P. A. Laferriere, C. J. Wetterer, L. P. Schelonka, M. A. Kramer, "Spatial-frequency selection using downconversion optical parametric amplification," J. Appl. Phys. 65, 3347-3350 (1989). [CrossRef]
- F. Devaux, E. Lantz, A. Lacourt, D. Gindre, H. Maillotte, P. A. Doreau, T. Laurent, "Picosecond parametric amplification of a monochromatic image," Nonlinear Opt. 11, 25-37 (1995).
- F. Devaux and E. Lantz, "Parametric amplification of a polychromatic image," J. Opt. Soc. Am. B 12, 2245-2252 (1995). [CrossRef]
- F. Devaux and E. Lantz, "Ultrahigh-speed imaging by parametric image amplification," Opt. Commun. 118, 25-27 (1995). [CrossRef]
- J. Watson, P. Georges, T. Lepine, B. Alonzi, A. Brun, "Imaging in diffuse media with ultrafast degenerate optical parametric amplification," Opt. Lett. 20, 231-233 (1995). [CrossRef] [PubMed]
- S. M. Cameron, D. E. Bliss, M. W. Kimmel, "Gated frequency-resolved optical imaging with an optical parametric amplifier for medical applications," Proc. SPIE 2679, 195-203 (1996). [CrossRef]
- E. Lantz and F. Devaux, "Parametric amplification of images," Quantum Semiclassic. Opt. 9, 279-286 (1997). [CrossRef]
- S.-K. Choi, M. L. Marable, and P. Kumar, "Observation of quantum noise correlations in parametric image amplification," in Quantum Electronics and Laser Science, Vol. 12 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C. 1997), pp. 94-95.
- O. Aytuer and P. Kumar, "Pulsed twin beams of light," Phys. Rev. Lett. 65, 1551-1554 (1990). [CrossRef] [PubMed]
- A. Gavrielides, P. Peterson, D. Cardimona, "Diffractive imaging in three-wave interactions," J. Appl. Phys. 62, 2640-2645 (1987). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.