Abstract
Holographic phase conjugation is analyzed as a method to create a photo-refractive lens with high numerical aperture. For this purpose a sub-wavelength hole is drilled into a metal surface directly on top of an iron-doped lithium niobate crystal. An interference pattern generated by the light coming from this point source and a plane reference wave is recorded. By using the phase-conjugated reference wave for read-out, a light wave being focused onto the former point source is reconstructed. In principle, a focusing system close to the theoretical diffraction limit could be implemented by this method. The performance of this arrangement is mainly determined by properties of the lithium niobate crystal, especially the crystal symmetry. Experimentally, the tight holographic focusing is demonstrated. The focus width of the reconstructed wave is shown to be below 1.2 μm, which is our spatial resolution. The diffraction efficiency obtained, however, is just 3×10−5 compared to 3×10−2 in the plane-wave case. This can be explained by experimental reasons, the inhomogeneous light intensity and limitations originating from the crystal symmetry. We estimate that the diffraction efficiency for phase conjugation through a sub-wavelength hole can be improved by three to four orders of magnitude by addressing the above-mentioned issues.
Similar content being viewed by others
References
J. Ma, B. Catanzaro, J.E. Ford, Y. Fainman, S.H. Lee, Photorefractive holographic lenses applications for dynamic focusing and dynamic image shifting. J. Opt. Soc. Am. A 11, 2471–2480 (1994)
W. Liu, D. Psaltis, Pixel size limit in holographic memories. Opt. Lett. 24, 1340–1342 (1999)
B.L. Volodin, B. Kippelen, K. Meerholz, B. Javidi, N. Peyghambarian, A polymeric optical pattern recognition system for security verification. Nature 383, 58–60 (1996)
Z. Yaqoob, D. Psaltis, M.S. Feld, C. Yang, Optical phase conjugation for turbidity suppression in biological samples. Nature Photonics 2, 110–115 (2008)
G. Barbastathis, M. Levene, D. Psaltis, Shift multiplexing with spherical reference waves. Appl. Opt. 35, 2403–2417 (1996)
B. Vohnson, S.I. Bozhevolnyi, Holographic approach to phase conjugation of optical near fields. J. Opt. Soc. Am. A 14, 1491–1499 (1997)
G. Lerosey, J. Rosney, A. Tourin, M. Fink, Focusing beyond the diffraction limit with far-field time reversal. Science 315, 1120–1122 (2007)
P. Günter, J.-P. Huignard (Eds.), Photorefractive materials and their applications. Springer series in optical sciences, vols. 1–3 (Springer, Berlin, 2005, 2006, 2007)
K. Buse, Light-induced charge transport processes in photorefractive crystals I: Models and experimental methods. Appl. Phys. B 64, 273–291 (1997)
K. Buse, Light-induced charge transport processes in photorefractive crystals II: Materials. Appl. Phys. B 64, 391–407 (1997)
H. Kurz, E. Krätzig, W. Keune, H. Engelmann, U. Gonser, B. Dischler, A. Räuber, Photorefractive centers in LiNbO3, studied by optical, Mössbauer, and EPR-methods. Appl. Phys. 12, 355–368 (1977)
H. Kogelnik, Coupled wave theory for thick hologram gratings. Bell Syst. Tech. J. 48, 2909–2947 (1969)
S. Tao, B. Wang, G.W. Burr, J. Chen, Diffraction efficiency of volume gratings with finite size: corrected analytical solution. J. Mod. Opt. 51, 1115–1122 (2004)
C. Genet, T.W. Ebbesen, Light in tiny holes. Nature 445, 39–46 (2007)
H.A. Bethe, Theory of diffraction by small holes. Phys. Rev. 66, 163 (1944)
N.V. Kukhtarev, Kinetics of hologram recording and erasure in electrooptic crystals. Sov. Tech. Phys. Lett. 2, 438–440 (1976)
F. Kalkum, K. Peithmann, K. Buse, Dynamics of holographic recording with focused beams in iron-doped lithium niobate crystals. Opt. Express 17, 1321–1329 (2009)
M. Jazbinsek, M. Zgonik, Material tensor parameters of LiNbO3 relevant for electro- and elasto-optics. Appl. Phys. B 74, 407–414 (2002)
K. Peithmann, A. Wiebrock, K. Buse, Photorefractive properties of highly-doped lithium niobate crystals in the visible near-infrared. Appl. Phys. B 68, 777–784 (1999)
S. Odoulov, Spatially oscillating photovoltaic current in iron-doped lithium niobate crystals. JETP Lett. 35, 10–13 (1982)
G. Montemezzani, M. Zgonik, Light diffraction at mixed phase and absorption gratings in anistrotropic media for arbitrary geometry. Phys. Rev. E 55, 1035–1047 (1996)
G.J. Steckman, W. Liu, R. Platz, D. Schroeder, C. Moser, F. Havermeyer, Volume holographic grating wavelength stabilized laser diodes. IEEE J. Sel. Top. Quantum Electron. 13, 672–678 (2007)
B.L. Volodin, S.V. Dolgy, E.D. Melnik, E. Downs, J. Shaw, V.S. Ban, Wavelength stabilization and spectrum narrowing of high-power multimode laser diodes and arrays by use of volume Bragg gratings. Opt. Lett. 29, 1891–1893 (2004)
T.Y. Chung, A. Rapaport, V. Smirnov, L.B. Glebov, M.C. Richardson, M. Bass, Solid-state laser spectral narrowing using a volumetric photothermal refractive Bragg grating cavity mirror. Opt. Lett. 31, 229–231 (2006)
S.J. Zilker, T. Bieringer, D. Haarer, R.S. Stein, J.W. van Egmond, S.G. Kostromine, Holographic data storage in amorphous polymers. Adv. Mater. 10, 855–859 (1998)
R. Hagen, T. Bieringer, Photoaddressable Polymers for optical data storage. Adv. Mater. 13, 1805–1810 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kalkum, F., Broch, S., Brands, T. et al. Holographic phase conjugation through a sub-wavelength hole. Appl. Phys. B 95, 637–645 (2009). https://doi.org/10.1007/s00340-009-3384-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00340-009-3384-4