OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 1 — Jan. 1, 2014
  • pp: 51–63

Probing limits on spatial resolution using nonlinear optical effects and nonclassical light

Y. Leng, D. H. Park, D. Schmadel, V. E. Yun, W. N. Herman, and J. Goldhar  »View Author Affiliations

Applied Optics, Vol. 53, Issue 1, pp. 51-63 (2014)

View Full Text Article

Enhanced HTML    Acrobat PDF (938 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Using a simple optical setup to detect and characterize transmission gratings in the far field, we demonstrate that going beyond the diffraction limit is not possible using linear interaction of nonclassical illumination with the target grating. We also confirm that nonlinear optical interactions with the target grating, or with the optical medium around it, do allow improvement in resolution.

© 2013 Optical Society of America

OCIS Codes
(190.1900) Nonlinear optics : Diagnostic applications of nonlinear optics
(270.5290) Quantum optics : Photon statistics
(180.4315) Microscopy : Nonlinear microscopy

ToC Category:
Nonlinear Optics

Original Manuscript: March 26, 2013
Revised Manuscript: November 18, 2013
Manuscript Accepted: November 25, 2013
Published: December 23, 2013

Y. Leng, D. H. Park, D. Schmadel, V. E. Yun, W. N. Herman, and J. Goldhar, "Probing limits on spatial resolution using nonlinear optical effects and nonclassical light," Appl. Opt. 53, 51-63 (2014)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Abbe, “Beiträge zur Theorie des Mikroskops und der Mikroskopischen Wahrnehmum,” Archiv für Mikroskopische Anatomie IX, 413–468 (1873).
  2. C. Cremer and B. R. Masters, “Resolution enhancement techniques in microscopy,” Eur. Phys. J. A 38, 281–344 (2013).
  3. A. J. den Dekker and A. van den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997). [CrossRef]
  4. J. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts and Company, 2005), p. 162.
  5. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University, 1997).
  6. G. T. di Francia, “Super-gain antennas and optical resolving power,” Supplemento AL Volume IX, Series IX DEL NUOVO CIMENTO, N. 3 (1952), pp. 426–438.
  7. H. Kim, G. W. Bryant, and S. J. Stranick, “Superresolution four-wave mixing microscopy,” Opt. Express 20, 6042–6051 (2012). [CrossRef]
  8. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit, Part 1,” J. Opt. Soc. Am. 56, 1463–1472 (1966). [CrossRef]
  9. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit. II,” J. Opt. Soc. Am. 57, 932–941 (1967). [CrossRef]
  10. A. Bachl and W. Lukosz, “Experiments on superresolution imaging of a reduced object field,” J. Opt. Soc. Am. 57, 163–169 (1967). [CrossRef]
  11. A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. G. Martinez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245–7251 (1999). [CrossRef]
  12. R. Heintzmann and C. Cremer, “Lateral modulated excitation microscopy: improvement of resolution by using a diffraction grating,” Proc. SPIE 3568, 185–196 (1999).
  13. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000). [CrossRef]
  14. B. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994). [CrossRef]
  15. K. Fujita, M. Kobayashi, S. Kawano, M. Yamanaka, and S. Kawata, “High-resolution confocal microscopy by saturated excitation of fluorescence,” Phys. Rev. Lett. 99, 228105 (2007). [CrossRef]
  16. M. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–795 (2006). [CrossRef]
  17. J. Renger, R. Quidant, N. van Hulst, and L. Novotny, “Surface-enhanced nonlinear four-wave mixing,” Phys. Rev. Lett. 104, 046803 (2010). [CrossRef]
  18. L. N. Guo, Z. L. Tang, and D. Xing, “Imaging theory of nonlinear Raman confocal microscopy,” J. Mod. Opt. 55, 375–386 (2008). [CrossRef]
  19. C. Barsi and J. W. Fleischer, “Increased field of view via nonlinear digital holography,” in Conference on Lasers and Electro-Optics 2010, OSA Technical Digest (CD) (Optical Society of America, 2010), paper CMCC4.
  20. Y. Leng, D. H. Park, V. Yun, P. Cho, W. N. Herman, and J. Goldhar, “Improvement in resolution using four-wave mixing in nonlinear confocal microscopy,” in CLEO: 2013 (Optical Society of America, 2013), paper JW2A.34.
  21. M. C. Teich and B. E. A. Saleh, “Entangled-photon microscopy,” translation of Mikroskopie s kvantove’ provazanymi fotony, Ceskoslovensky casopis pro fyziku 47, 3–8 (1997).
  22. A. Muthukrishnan, M. O. Scully, and M. S. Zubairy, “Quantum microscopy using photon correlations,” J. Opt. B 6, S575–S582 (2004).
  23. S. J. Bentley, R. W. Boyd, E. M. Nagasako, and G. S. Agarwal, “Quantum entanglement for optical lithography and microscopy beyond the Rayleigh limit,” in Quantum Electronics and Laser Science Conference (The Optical Society, 2001), paper QTuD2.
  24. M. D’Angelo, M. V. Chekhova, and Y. Shih, “Two-photon diffraction and quantum lithography,” Phys. Rev. Lett. 87, 013602 (2001). [CrossRef]
  25. V. Giovannetti, S. Lloyd, L. Maccone, and J. H. Shapiro, “Sub-Rayleigh-diffraction-bound imaging,” Phys. Rev. A 79, 1003782 (2009).
  26. Y. Kawabe, H. Fujiwara, R. Okamoto, K. Sasaki, and S. Takeuchi, “Quantum interference fringes beating the diffraction limit,” Opt. Express 15, 14244–14250 (2007). [CrossRef]
  27. L. Lugiato, A. Gatti, and E. Brambilla, “Quantum imaging,” J. Opt. B 4, 176–183 (2002).
  28. J. Jacobson, G. Björk, I. Chuang, and Y. Yamamoto, “Photonic de Broglie waves,” Phys. Rev. Lett. 74, 4835–4838 (1995). [CrossRef]
  29. Y.-S. Kim, O. Kwon, S. M. Lee, J.-C. Lee, H. Kim, S.-K. Choi, H. S. Park, and Y.-H. Kim, “Observation of Young’s double-slit interference with the three-photon N00N state,” Opt. Express 19, 24957–24966 (2011). [CrossRef]
  30. J. P. Dowling, “Quantum optical metrology—the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [CrossRef]
  31. I. Afek, O. Ambar, and Y. Silberberg, “High-NOON states by mixing quantum and classical light,” Science 328, 879–881 (2010). [CrossRef]
  32. F. Sciarrino, C. Vitelli, F. DeMartini, R. Glasser, H. Cable, and J. P. Dowling, “Experimental sub-Rayleigh resolution by an unseeded high-gain optical parametric amplifier for quantum lithography,” Phys. Rev. A 77, 012324 (2008). [CrossRef]
  33. A. A. Maznev, K. A. Nelson, and J. A. Rogers, “Optical heterodyne detection of laser-induced gratings,” Opt. Lett. 23, 1319–1321 (1998). [CrossRef]
  34. A. A. Maznev, T. F. Crimmins, and K. A. Nelson, “How to make femtosecond pulses overlap,” Opt. Lett. 23, 1378–1380 (1998). [CrossRef]
  35. G. S. Agarwal, K. W. Chan, R. W. Boyd, H. Cable, and J. P. Dowling, “Quantum states of light produced by a high-gain optical parametric amplifier for use in quantum lithography,” J. Opt. Soc. Am. B 24, 270–274 (2007). [CrossRef]
  36. H. Cable, R. Vyas, S. Singh, and J. P. Dowling, “An optical parametric oscillator as a high-flux source of two-mode light for quantum lithography,” New J. Phys. 11, 113055 (2009). [CrossRef]
  37. G. Cerullo and S. De Silvetri, “Ultrafast optical parametric amplifiers,” Rev. Sci. Instrum. 74(1), 1–18 (2003). [CrossRef]
  38. B. R. Mollow and R. J. Glauber, “Quantum theory of parametric amplification. I,” Phys. Rev. 160, 1076–1096 (1967). [CrossRef]
  39. H. Kogelnik, “Coupled-wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969). [CrossRef]
  40. W. Cao, Y.-H. Peng, Y. Leng, C. H. Lee, W. N. Herman, and J. Goldhar, “Phase scan technique for measuring phase of complex χ(3) of nonlinear polymer thin films,” in Organic Thin Films for Photonics Applications, W. N. Herman, S. Flom, and S. Foulger, eds. (ACS Symposium Series Books, 2010), Chap. 10.
  41. R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford University, 2000).
  42. R. Shimizu, K. Edamatsu, and T. Itoh, “Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis,” Phys. Rev. A 74, 013801 (2006). [CrossRef]
  43. C. C. Gerry and P. L. Knight, Introductory Quantum Optics (Cambridge University, 2004), Section 6.2.
  44. H. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, 2000).
  45. J. B. Ashcom, R. R. Gattass, C. B. Schaffer, and E. Mazur, “Numerical aperture dependence of damage and supercontinuum generation from femtosecond laser pulses in bulk fused silica,” J. Opt. Soc. Am. B 23, 2317–2322 (2006). [CrossRef]
  46. W. Lukosz and M. Marchand, “Optischen Abbildung Unter Überschreitung der Beugungsbedingten Auflösungsgrenze,” Optica Acta 10, 241–255 (1963). [CrossRef]
  47. C. W. McCutchen, “Superresolution in microscopy and the Abbe resolution limit,” J. Opt. Soc. Am. 57, 1190–1192 (1967). [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.

CrossCheck Deposited