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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 5 — Mar. 10, 2014
  • pp: 6114–6132

5D-Tracking of a nanorod in a focused laser beam - a theoretical concept

Markus Grießhammer and Alexander Rohrbach  »View Author Affiliations

Optics Express, Vol. 22, Issue 5, pp. 6114-6132 (2014)

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Back-focal plane (BFP) interferometry is a very fast and precise method to track the 3D position of a sphere within a focused laser beam using a simple quadrant photo diode (QPD). Here we present a concept of how to track and recover the 5D state of a cylindrical nanorod (3D position and 2 tilt angles) in a laser focus by analyzing the interference of unscattered light and light scattered at the cylinder. The analytical theoretical approach is based on Rayleigh-Gans scattering together with a local field approximation for an infinitely thin cylinder. The approximated BFP intensities compare well with those from a more rigorous numerical approach. It turns out that a displacement of the cylinder results in a modulation of the BFP intensity pattern, whereas a tilt of the cylinder results in a shift of this pattern. We therefore propose the concept of a local QPD in the BFP of a detection lens, where the QPD center is shifted by the angular coordinates of the cylinder tilt.

© 2014 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(140.7010) Lasers and laser optics : Laser trapping
(260.3160) Physical optics : Interference
(290.0290) Scattering : Scattering

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: November 27, 2013
Revised Manuscript: February 6, 2014
Manuscript Accepted: February 7, 2014
Published: March 7, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Markus Grießhammer and Alexander Rohrbach, "5D-Tracking of a nanorod in a focused laser beam - a theoretical concept," Opt. Express 22, 6114-6132 (2014)

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  1. A. P. Bartko, R. M. Dickson, “Imaging three-dimensional single molecule orientations,” J. Phys. Chem. B 103(51), 11237–11241 (1999). [CrossRef]
  2. K. I. Mortensen, L. S. Churchman, J. A. Spudich, H. Flyvbjerg, “Optimized localization analysis for single-molecule tracking and super-resolution microscopy,” Nat. Methods 7(5), 377–381 (2010). [CrossRef] [PubMed]
  3. S. Stallinga, B. Rieger, “Position and orientation estimation of fixed dipole emitters using an effective Hermite point spread function model,” Opt. Express 20(6), 5896–5921 (2012). [CrossRef] [PubMed]
  4. M. Böhmer, J. Enderlein, “Orientation imaging of single molecules by wide-field epifluorescence microscopy,” J. Opt. Soc. Am. B 20(3), 554–559 (2003). [CrossRef]
  5. P. J. Pauzauskie, A. Radenovic, E. Trepagnier, H. Shroff, P. D. Yang, J. Liphardt, “Optical trapping and integration of semiconductor nanowire assemblies in water,” Nat. Mater. 5(2), 97–101 (2006). [CrossRef] [PubMed]
  6. M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394(6691), 348–350 (1998). [CrossRef]
  7. E. L. Florin, J. K. H. Horber, E. H. K. Stelzer, “High-resolution axial and lateral position sensing using two-photon excitation of fluorophores by a continuous-wave Nd alpha YAG laser,” Appl. Phys. Lett. 69(4), 446–448 (1996). [CrossRef]
  8. P. C. Seitz, E. H. K. Stelzer, A. Rohrbach, “Interferometric tracking of optically trapped probes behind structured surfaces: a phase correction method,” Appl. Opt. 45(28), 7309–7315 (2006). [CrossRef] [PubMed]
  9. Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447(7148), 1098–1101 (2007). [CrossRef] [PubMed]
  10. D. B. Phillips, J. A. Grieve, S. N. Olof, S. J. Kocher, R. Bowman, M. J. Padgett, M. J. Miles, D. M. Carberry, “Surface imaging using holographic optical tweezers,” Nanotechnology 22(28), 285503 (2011). [CrossRef] [PubMed]
  11. A. A. M. Bui, A. B. Stilgoe, T. A. Nieminen, H. Rubinsztein-Dunlop, “Calibration of nonspherical particles in optical tweezers using only position measurement,” Opt. Lett. 38(8), 1244–1246 (2013). [CrossRef] [PubMed]
  12. S. J. Parkin, G. Knöner, T. A. Nieminen, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Picoliter viscometry using optically rotated particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76(4), 041507 (2007). [CrossRef] [PubMed]
  13. D. G. Grier, “A revolution in optical manipulation,” Nature 424(6950), 810–816 (2003). [CrossRef] [PubMed]
  14. M. Speidel, L. Friedrich, A. Rohrbach, “Interferometric 3D tracking of several particles in a scanning laser focus,” Opt. Express 17(2), 1003–1015 (2009). [CrossRef] [PubMed]
  15. D. Ruh, B. Tränkle, A. Rohrbach, “Fast parallel interferometric 3D tracking of numerous optically trapped particles and their hydrodynamic interaction,” Opt. Express 19(22), 21627–21642 (2011). [CrossRef] [PubMed]
  16. K. Dholakia, T. Cizmar, “Shaping the future of manipulation,” Nat. Photonics 5(6), 335–342 (2011). [CrossRef]
  17. S. H. Simpson, S. Hanna, “Optical trapping of spheroidal particles in Gaussian beams,” J. Opt. Soc. Am. A 24(2), 430–443 (2007). [CrossRef] [PubMed]
  18. F. Borghese, P. Denti, R. Saija, M. A. Iati, O. M. Marago, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100, 163903 (2008).
  19. P. B. Bareil, Y. Sheng, “Angular and position stability of a nanorod trapped in an optical tweezers,” Opt. Express 18(25), 26388–26398 (2010). [CrossRef] [PubMed]
  20. S. H. Simpson, S. Hanna, “First-order nonconservative motion of optically trapped nonspherical particles,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 82(3), 031141 (2010). [CrossRef] [PubMed]
  21. Y. Cao, A. B. Stilgoe, L. Chen, T. A. Nieminen, H. Rubinsztein-Dunlop, “Equilibrium orientations and positions of non-spherical particles in optical traps,” Opt. Express 20(12), 12987–12996 (2012). [CrossRef] [PubMed]
  22. A. Irrera, P. Artoni, R. Saija, P. G. Gucciardi, M. A. Iatì, F. Borghese, P. Denti, F. Iacona, F. Priolo, O. M. Maragò, “Size-scaling in optical trapping of silicon nanowires,” Nano Lett. 11(11), 4879–4884 (2011). [CrossRef] [PubMed]
  23. P. J. Reece, W. J. Toe, F. Wang, S. Paiman, Q. Gao, H. H. Tan, C. Jagadish, “Characterization of semiconductor nanowires using optical tweezers,” Nano Lett. 11(6), 2375–2381 (2011). [CrossRef] [PubMed]
  24. O. M. Maragò, P. H. Jones, F. Bonaccorso, V. Scardaci, P. G. Gucciardi, A. G. Rozhin, A. C. Ferrari, “Femtonewton force sensing with optically trapped nanotubes,” Nano Lett. 8(10), 3211–3216 (2008). [CrossRef] [PubMed]
  25. L. Dixon, F. C. Cheong, D. G. Grier, “Holographic deconvolution microscopy for high-resolution particle tracking,” Opt. Express 19(17), 16410–16417 (2011). [CrossRef] [PubMed]
  26. A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, J. K. H. Hörber, “Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light,” Microsc. Res. Tech. 44(5), 378–386 (1999). [CrossRef] [PubMed]
  27. A. Rohrbach, C. Tischer, D. Neumayer, E. L. Florin, E. H. K. Stelzer, “Trapping and tracking a local probe with a photonic force microscope,” Rev. Sci. Instrum. 75(6), 2197–2210 (2004). [CrossRef]
  28. G. Volpe, G. Kozyreff, D. Petrov, “Backscattering position detection for photonic force microscopy,” J. Appl. Phys. 102(8), 084701 (2007). [CrossRef]
  29. R. Huang, I. Chavez, K. M. Taute, B. Lukic, S. Jeney, M. G. Raizen, E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nat. Phys. 7(7), 576–580 (2011). [CrossRef]
  30. L. Friedrich, A. Rohrbach, “Improved interferometric tracking of trapped particles using two frequency-detuned beams,” Opt. Lett. 35(11), 1920–1922 (2010). [CrossRef] [PubMed]
  31. H. Kress, E. H. K. Stelzer, A. Rohrbach, “Tilt angle dependent three-dimensional-position detection of a trapped cylindrical particle in a focused laser beam,” Appl. Phys. Lett. 84(21), 4271–4273 (2004). [CrossRef]
  32. L. Friedrich, A. Rohrbach, “Tuning the detection sensitivity: a model for axial backfocal plane interferometric tracking,” Opt. Lett. 37(11), 2109–2111 (2012). [CrossRef] [PubMed]
  33. A. Rohrbach, E. H. K. Stelzer, “Optical trapping of dielectric particles in arbitrary fields,” J. Opt. Soc. Am. A 18(4), 839–853 (2001). [CrossRef] [PubMed]
  34. M. M. Tirado, C. L. Martinez, J. G. Delatorre, “Comparison of theories for the translational and rotational diffusion coefficients of rod-like macromolecules. Applications to short DNA fragments,” J. Chem. Phys. 81(4), 2047–2052 (1984). [CrossRef]
  35. A. Rohrbach, H. Kress, E. H. K. Stelzer, “Three-dimensional tracking of small spheres in focused laser beams: influence of the detection angular aperture,” Opt. Lett. 28(6), 411–413 (2003). [CrossRef] [PubMed]
  36. M. Pelton, M. Z. Liu, H. Y. Kim, G. Smith, P. Guyot-Sionnest, N. F. Scherer, “Optical trapping and alignment of single gold nanorods by using plasmon resonances,” Opt. Lett. 31(13), 2075–2077 (2006). [CrossRef] [PubMed]
  37. C. Selhuber-Unkel, I. Zins, O. Schubert, C. Sönnichsen, L. B. Oddershede, “Quantitative optical trapping of single gold nanorods,” Nano Lett. 8(9), 2998–3003 (2008). [CrossRef] [PubMed]

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