Abstract

We demonstrate theoretically and experimentally an anomaly in the intensity distribution at the focal region of a Laguerre-Gaussian beam, when such a beam is focused by a high numerical aperture objective lens through an index-mismatched interface satisfying the total internal reflection condition. An asymmetric rotation of the focal field arising from the interplay of the phase shift induced by the total internal reflection and the helical phase of the Laguerre-Gaussian beam has been experimentally observed by a scanning near-field optical microscope. A cross-section analysis shows that the experimental results match well with the theoretical predictions.

© 2005 Optical Society of America

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References

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Appl. Opt. (1)

Appl. Phys. Lett. (2)

M. Gu, J.-B. Haumonte, Y. M., J. W. M. Chon, and X. Gan, "Laser trapping and manipulation under focused evanescent wave illumination," Appl. Phys. Lett. 84, 4236-4238 (2004).
[CrossRef]

B. Jia, X. Gan, and M. Gu, "Direct observation of a pure focused evanescent field of a high numerical aperture objective lens by scanning near-field optical microscopy," Appl. Phys. Lett. 86, 131110, (2005).
[CrossRef]

Biophys. Res. Commun. (1)

M. Tokunaga, K. Kitamura, K. Saito, A. H. Iwane and T. Yanagida, Biochem. "Single molecule imaging of fluorophores and enzymatic reactions achieved by objective-type total internal reflection fluorescence microscopy," Biophys. Res. Commun. 235, 47-53 (1997).
[CrossRef]

J. Appl. Phys (1)

N. Hayazawa, A. Tarun, Y. Inouye, and S. Kawata, "Near-field enhanced Raman spectroscopy using side illumination optics," J. Appl. Phys. 92, 6983-6986 (2002).
[CrossRef]

J. of Microsc. (1)

K. Bahlmann and S. W. Hell, "Electric field depolarization in high aperture focusing with emphasis on annular apertures," J. of Microsc. 200, 59-67 (2000).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

D. G. Grier, "A revolution in optical manipulation," Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Express (6)

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical-vector beams," Opt. Express 7, 77-87 (2000), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-2-77">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-7-2-77</a>
[CrossRef] [PubMed]

B. Jia, X. Gan, and M. Gu, "Direct measurement of a radially polarized focused evanescent field facilitated by a single LCD, " Opt. Express 13, 6821-6827 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6821">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6821</a>
[CrossRef] [PubMed]

D. Ganic, X. Gan, and Min Gu, "Trapping force and optical lifting under focused evanescent wave illumination," Opt. Express 12, 5533-5538 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5533">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5533</a>
[CrossRef] [PubMed]

C. A. Alonzo, P. J. Rodrigo, and J. Glückstad, "Helico-conical optical beams: a product of helical and conical phase fronts," Opt. Express 13, 1749-1760 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1749">www.opticsexpress.org/abstract.cfm?URI=OPEX-13-5-1749</a.
[CrossRef] [PubMed]

D. Ganic, X. Gan, and M. Gu, "Optical trapping force with annular and doughnut laser beams based on vectorial diffraction," Opt. Express 13, 1260-1265 (2005), <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1260">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-4-1260. </a>

D. Ganic, X. Gan, and M. Gu, "Focusing of doughnut laser beams by a high numerical-aperture objective in free space," Opt. Express 11, 2747-2752 (2003), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2747">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-11-21-2747</a>
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (4)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a Laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

K. Okamoto and S. Kawata, "Radiation force exerted on subwavelength particles near a nanoaperture," Phys. Rev. Lett. 83, 4534-4537 (1999).
[CrossRef]

L. Novotny, R. X. Bian, and X. S. Xie, "Theory of nanometric optical tweezers," Phys. Rev. Lett. 79, 645-648 (1997).
[CrossRef]

B. Sick, B. Hecht, and L. Novotny, "Orientational imaging of single molecules by annular illumination, " Phys. Rev. Lett. 85, 4482-4485 (2000).
[CrossRef] [PubMed]

Proc. Phys. Soc. (1)

H. H. Hopkins, "The airy disc formula for systems of high relative aperture," Proc. Phys. Soc. 55, 116-128 (1943).
[CrossRef]

Science (2)

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

L. Paterson, M. P. MacDonald, J. Arlt, W. Sibbett, P. E. Bryant, and K. Dholakia, "Controlled rotation of optically trapped microscopic particles," Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Other (2)

E. Hecht and A. Zajac, Optics (Addison-Wesley Publishing Company, U. S. A, 2002)

M. Gu, Advanced Optical Imaging Theory (Springer, Heidelberg, 2000).

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Figures (4)

Fig. 1.
Fig. 1.

Schematic for the phase shift generated by a high NA objective (NA=1.65, 100×) at the coverglass (n1=1.78) and air (n2=1) interface under the TIR condition and its interaction with the helical phase pattern of an LG beam (n=1). (a) Incident helical phase front of the LG beam, (b) obstructed by a circular opaque disk (OBS) to produce a focused evanescent field (ρ is the radius of the obstruction disk normalized by the size of the back aperture of the objective (OBJ). ρc is the critical radius, corresponding to the critical angle (θc in this case)), (c) phase shift β induced by TIR versus the normalized obstruction radius ρ. (d) Equivalent phase dislocation of the LG beam at the back aperture of the objective after adding up the phase shift β shown in (c).

Fig. 2.
Fig. 2.

Intensity distributions in the focal region of the objective (NA=1.65) at the coverglass (n1=1.78) and air (n2=1) interface under the illumination of LG beams with topological charges (a) n=0, (b) n=1, (c) n=2, (d) n=3. Each Fig. has been normalized to its maximum intensity. The arrow indicates the incident polarization direction.

Fig. 3.
Fig. 3.

(a) The experimental setup for the characterization of focused evanescent LG beams with a SNOM probe. QWP: quarter wave plate, P: polarizer, BE: beam expansion system, SLM: special light modulator, BS: beam splitter, M: mirror, L1, L2, L3: lenses, OBS: obstruction (ε=0.803), OBJ: objective, NA=1.65, 100 × , CG: special coverglass (n=1.78) mounted on top of a three-dimensional scanning stage, Pre-Arm: pre-amplifier, CCD: charge-coupled device. (b) Phase pattern loaded on the SLM to generate a doughnut beam with topological charge 1.

Fig. 4.
Fig. 4.

Comparison between the experimental cross-sections of the normalized intensity distributions in the focal region of an objective with NA=1.65 at the coverglass (n1=1.78) and air (n2=1) interface for LG beams with n=0-3 with the theoretical calculations (a) along the incident polarization direction, (b-d) across the two peak intensity points. The insets on the left side of each Fig. show the measured focal intensity distributions, On the right side the theoretical simulations are presented. The arrow indicates the incident polarization direction. Scale bar: 500 nm.

Equations (1)

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φ d = + β ( ρ ) ρ c < ρ < 1

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