OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26710–26724

Spatial modes of phase-sensitive parametric image amplifiers with circular and elliptical Gaussian pumps

Muthiah Annamalai, Nikolai Stelmakh, Michael Vasilyev, and Prem Kumar  »View Author Affiliations

Optics Express, Vol. 19, Issue 27, pp. 26710-26724 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (3160 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We develop a method for finding the number and shapes of the independently squeezed or amplified modes of a spatially-broadband, travelling-wave, frequency- and polarization-degenerate optical parametric amplifier in the general case of an elliptical Gaussian pump. The obtained results show that for tightly focused pump only one mode is squeezed, and this mode has a Gaussian TEM00 shape. For larger pump spot sizes that support multiple modes, the shapes of the most-amplified modes are close to Hermite- or Laguerre-Gaussian profiles. These results can be used to generate matched local oscillators for detecting high amounts of squeezing and to design parametric image amplifiers that introduce minimal distortion.

© 2011 OSA

OCIS Codes
(190.4970) Nonlinear optics : Parametric oscillators and amplifiers
(270.6570) Quantum optics : Squeezed states

ToC Category:
Nonlinear Optics

Original Manuscript: September 22, 2011
Revised Manuscript: November 23, 2011
Manuscript Accepted: November 28, 2011
Published: December 14, 2011

Muthiah Annamalai, Nikolai Stelmakh, Michael Vasilyev, and Prem Kumar, "Spatial modes of phase-sensitive parametric image amplifiers with circular and elliptical Gaussian pumps," Opt. Express 19, 26710-26724 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. C. M. Caves, “Quantum limits on noise in linear amplifiers,” Phys. Rev. D Part. Fields 26(8), 1817–1839 (1982). [CrossRef]
  2. D. Levandovsky, M. Vasilyev, and P. Kumar, “Amplitude squeezing of light by means of a phase-sensitive fiber parametric amplifier,” Opt. Lett. 24(14), 984–986 (1999). [CrossRef] [PubMed]
  3. D. Levandovsky, M. Vasilyev, and P. Kumar, “Near-noiseless amplification of light by a phase-sensitive fibre amplifier,” PRAMANA–J. Phys. 56(2-3), 281–285 (2001). [CrossRef]
  4. W. Imajuku, A. Takada, and Y. Yamabayashi, “Low-noise amplification under the 3 dB noise figure in high-gain phase-sensitive fibre amplifier,” Electron. Lett. 35(22), 1954–1955 (1999). [CrossRef]
  5. P. L. Voss, K. G. Köprülü, and P. Kumar, “Raman-noise-induced quantum limits for χ(3) nondegenerate phase-sensitive amplification and quadrature squeezing,” J. Opt. Soc. Am. B 23(4), 598–610 (2006). [CrossRef]
  6. Z. Tong, A. Bogris, C. Lundström, C. J. McKinstrie, M. Vasilyev, M. Karlsson, and P. A. Andrekson, “Modeling and measurement of the noise figure of a cascaded non-degenerate phase-sensitive parametric amplifier,” Opt. Express 18(14), 14820–14835 (2010). [CrossRef] [PubMed]
  7. M. I. Kolobov and L. A. Lugiato, “Noiseless amplification of optical images,” Phys. Rev. A 52(6), 4930–4940 (1995). [CrossRef] [PubMed]
  8. M. Kolobov, “The spatial behavior of nonclassical light,” Rev. Mod. Phys. 71(5), 1539–1589 (1999). [CrossRef]
  9. K. Wang, G. Yang, A. Gatti, and L. Lugiato, “Controlling the signal-to-noise ratio in optical parametric image amplification,” J. Opt. B Quantum Semiclassical Opt. 5(4), S535–S544 (2003). [CrossRef]
  10. S.-K. Choi, M. Vasilyev, and P. Kumar, “Noiseless optical amplification of images,” Phys. Rev. Lett. 83, 1938–1941 (1999) [erratum: Phys. Rev. Lett. 84, 1361–1361 (2000)].
  11. A. Mosset, F. Devaux, and E. Lantz, “Spatially noiseless optical amplification of images,” Phys. Rev. Lett. 94(22), 223603 (2005). [CrossRef] [PubMed]
  12. E. Lantz and F. Devaux, “Parametric amplification of images: from time gating to noiseless amplification,” IEEE J. Sel. Top. Quantum Electron. 14(3), 635–647 (2008). [CrossRef]
  13. L. Lopez, N. Treps, B. Chalopin, C. Fabre, and A. Maître, “Quantum processing of images by continuous wave optical parametric amplification,” Phys. Rev. Lett. 100(1), 013604 (2008). [CrossRef] [PubMed]
  14. P. Kumar, V. Grigoryan, and M. Vasilyev, “Noise-free amplification: towards quantum laser radar,” the 14th Coherent Laser Radar Conference, Snowmass, CO, July 2007. http://space.hsv.usra.edu/CLRC/presentations/Kumar.ppt
  15. Z. Dutton, J. H. Shapiro, and S. Guha, “LADAR resolution improvement using receivers enhanced with squeezed-vacuum injection and phase-sensitive amplification,” J. Opt. Soc. Am. B 27(6), A63–A72 (2010). [CrossRef]
  16. O.-K. Lim, G. Alon, Z. Dutton, S. Guha, M. Vasilyev, and P. Kumar, “Optical resolution enhancement with phase-sensitive preamplification,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CTuPP7.
  17. M. Vasilyev, N. Stelmakh, and P. Kumar, “Phase-sensitive image amplification with elliptical Gaussian pump,” Opt. Express 17(14), 11415–11425 (2009). [CrossRef] [PubMed]
  18. M. Vasilyev, N. Stelmakh, and P. Kumar, “Estimation of the spatial bandwidth of an optical parametric amplifier with plane-wave pump,” J. Mod. Opt. 56(18-19), 2029–2033 (2009). [CrossRef]
  19. A. La Porta and R. E. Slusher, “Squeezing limits at high parametric gains,” Phys. Rev. A 44(3), 2013–2022 (1991). [CrossRef] [PubMed]
  20. S.-K. Choi, R.-D. Li, C. Kim, and P. Kumar, “Traveling-wave optical parametric amplifier: investigation of its phase-sensitive and phase-insensitive gain response,” J. Opt. Soc. Am. B 14(7), 1564–1575 (1997). [CrossRef]
  21. C. Kim and P. Kumar, “Quadrature-squeezed light detection using a self-generated matched local oscillator,” Phys. Rev. Lett. 73(12), 1605–1608 (1994). [CrossRef] [PubMed]
  22. R.-D. Li, S.-K. Choi, C. Kim, and P. Kumar, “Generation of sub-Poissonian pulses of light,” Phys. Rev. A 51(5), R3429–R3432 (1995). [CrossRef] [PubMed]
  23. K. G. Köprülü and O. Aytür, “Analysis of Gaussian-beam degenerate optical parametric amplifiers for the generation of quadrature-squeezed states,” Phys. Rev. A 60(5), 4122–4134 (1999). [CrossRef]
  24. K. G. Köprülü and O. Aytür, “Analysis of the generation of amplitude-squeezed light with Gaussian-beam degenerate optical parametric amplifiers,” J. Opt. Soc. Am. B 18(6), 846–854 (2001). [CrossRef]
  25. C. Schwob, P. F. Cohadon, C. Fabre, M. A. M. Marte, H. Ritsch, A. Gatti, and L. Lugiato, “Transverse effects and mode couplings in OPOs,” Appl. Phys. B 66(6), 685–699 (1998). [CrossRef]
  26. M. Annamalai, N. Stelmakh, M. Vasilyev, and P. Kumar, “Spatial modes of phase-sensitive image amplifier with elliptical Gaussian pump,” in Laser Science, OSA Technical Digest (CD) (Optical Society of America, 2010), paper LTuB5.
  27. M. Vasilyev, M. Annamalai, N. Stelmakh, and P. Kumar, “Quantum properties of a spatially-broadband traveling-wave phase-sensitive optical parametric amplifier,” J. Mod. Opt. 57(19), 1908–1915 (2010). [CrossRef]
  28. Please note that the definition of deff in our prior work (Refs. 17, 18, and 27) is different from that in the present paper. The prior-work deff denotes the quantity that is more commonly known as the effective χ(2) and equals 2deff in the present paper’s notations. As a result, the nonlinear paraxial wave equation in Refs. 17, 18, and 27 does not have the factor of 2 in front of deff. One fallout of this unfortunate choice of notation in our prior work is that Ref. 17 assumes effective χ(2) = 8.7 pm/V for PPKTP crystal, which is about half of the actual value of that crystal’s nonlinearity, and the resulting pump powers listed in Refs. 17 and 26 are four times larger than those required for the same gain in a real PPKTP crystal. The present paper’s definitions rectify the previous inconsistencies.
  29. E. Lantz and F. Devaux, “Numerical simulation of spatial fluctuations in parametric image amplification,” Eur. Phys. J. D 17(1), 93–98 (2001). [CrossRef]
  30. H. P. Yuen, “Two-photon coherent states of the radiation field,” Phys. Rev. A 13(6), 2226–2243 (1976). [CrossRef]
  31. H. P. Yuen, “Multimode two-photon coherent states and unitary representation of the symplectic group,” Nucl. Phys. B 6, 309–313 (1989). [CrossRef]
  32. D. Levandovsky, “Quantum noise suppression using optical fibers,” Ph.D. thesis, Northwestern University, 1999.
  33. L. Lopez, S. Gigan, N. Treps, A. Maître, C. Fabre, and A. Gatti, “Multimode squeezing properties of a confocal optical parametric oscillator: Beyond the thin-crystal approximation,” Phys. Rev. A 72(1), 013806 (2005). [CrossRef]
  34. M. Annamalai, M. Vasilyev, N. Stelmakh, and P. Kumar, “Compact Representation of Spatial Modes of Phase-Sensitive Image Amplifier,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JThB77.
  35. W. Wasilewski, A. I. Lvovsky, K. Banaszek, and C. Radzewicz, “Pulsed squeezed light: Simultaneous squeezing of multiple modes,” Phys. Rev. A 73(6), 063819 (2006). [CrossRef]
  36. J. H. Shapiro and A. Shakeel, “Optimizing homodyne detection of quadrature-noise squeezing by local-oscillator selection,” J. Opt. Soc. Am. B 14(2), 232–249 (1997). [CrossRef]
  37. C. J. McKinstrie, “Unitary and singular value decompositions of parametric processes in fibers,” Opt. Commun. 282(4), 583–593 (2009). [CrossRef]
  38. G. Patera, N. Treps, C. Fabre, and G. J. de Valcárcel, “Quantum theory of synchronously pumped type I optical parametric oscillators: characterization of the squeezed supermodes,” Eur. Phys. J. D 56(1), 123–140 (2010). [CrossRef]
  39. A. Ekert and P. L. Knight, “Entangled quantum systems and the Schmidt decomposition,” Am. J. Phys. 63(5), 415–423 (1995). [CrossRef]
  40. C. K. Law, I. A. Walmsley, and J. H. Eberly, “Continuous frequency entanglement: effective finite hilbert space and entropy control,” Phys. Rev. Lett. 84(23), 5304–5307 (2000). [CrossRef] [PubMed]
  41. C. K. Law and J. H. Eberly, “Analysis and interpretation of high transverse entanglement in optical parametric down conversion,” Phys. Rev. Lett. 92(12), 127903 (2004). [CrossRef] [PubMed]

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.

CrossCheck Deposited