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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 5 — May. 1, 2000
  • pp: 858–866

Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications

Fadi I. Baida, Daniel Van Labeke, and Jean-Marie Vigoureux  »View Author Affiliations

JOSA A, Vol. 17, Issue 5, pp. 858-866 (2000)

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Longitudinal and transverse shifts of a light beam at total internal reflection was experimentally studied by far-field measurements on the reflected field. We propose to use a scanning tunneling optical microscope (STOM) to study these shifts in transmission, and we present a theoretical model of this proposed experiment to obtain a numerical estimation of these shifts. We study the reflection and the transmission of a three-dimensional polarized incident beam. We verify the validity of our formalism by studying the Goos–Hanchen shift in reflection and by comparing our results with published ones. Then we calculate STOM images of the transmitted field distribution. On the images the well-known Goos–Hanchen shift is easily observed. But we also encounter a smaller shift, perpendicular to the plane of incidence. This transverse shift was also observed in reflection by Imbert and Levy [Nouv. Rev. Opt. 6, 285 (1975)]. We study the variations of the two shifts versus various parameters such as the angle of incidence, the optical index, and the incident polarization. Then we discuss the feasibility of the near-field observation of these shifts.

© 2000 Optical Society of America

OCIS Codes
(180.5810) Microscopy : Scanning microscopy
(240.7040) Optics at surfaces : Tunneling
(260.2110) Physical optics : Electromagnetic optics
(260.6970) Physical optics : Total internal reflection

Original Manuscript: May 26, 1999
Revised Manuscript: October 13, 1999
Manuscript Accepted: December 13, 1999
Published: May 1, 2000

Fadi I. Baida, Daniel Van Labeke, and Jean-Marie Vigoureux, "Numerical study of the displacement of a three-dimensional Gaussian beam transmitted at total internal reflection. Near-field applications," J. Opt. Soc. Am. A 17, 858-866 (2000)

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  1. F. Goos, H. Hanchen, “Ein neuer and fundamentaler Versuch zur total Reflection,” Ann. Phys. (Leipzig) 1, 333–345 (1947). [CrossRef]
  2. M. A. Porras, “Nonspecular reflection of general light beams at a dielectric interface,” Opt. Commun. 135, 369–377 (1997). [CrossRef]
  3. L. I. Perez, F. Ciocci, “Nonspecular first-order effects in Kretschmann’s configuration,” J. Mod. Opt. 45, 2487–2502 (1998). [CrossRef]
  4. W. Nasalski, “Longitudinal and transverse effects of nonspecular reflection,” J. Opt. Soc. Am. A 13, 172–181 (1996). [CrossRef]
  5. C. Imbert, Y. Levy, “Déplacement d’un faisceau lumineux par réflexion totale: filtrage des états de polarisation et amplification,” Nouv. Rev. Opt. 6, 285–296 (1975). [CrossRef]
  6. J. J. Cowan, B. Anicin, “Longitudinal and transverse displacements of a bounded microwave beam at total internal reflection,” J. Opt. Soc. Am. 67, 1307–1314 (1977). [CrossRef]
  7. L. Dutriaux, A. L. Floch, F. Bretenaker, “Measurement of the transverse displacement at total reflection by helicoidal laser eigenstates,” Europhys. Lett. 24, 345–349 (1993). [CrossRef]
  8. Y. Levy, C. Imbert, “Amplification des déplacements à la réflexion totale,” Opt. Commun. 13, 43–47 (1975). [CrossRef]
  9. F. Bretenaker, A. L. Floch, L. Dutriaux, “Direct measurement of the optical Goos–Hanchen effect in lasers,” Phys. Rev. Lett. 68, 931–933 (1992). [CrossRef] [PubMed]
  10. D. Van Labeke, D. Barchiesi, “Theoretical problems in scanning near-field optical microscopy,” in Near Field Optics, D. W. Pohl, D. Courjon, eds., Vol. 242 of NATO Advanced Science Institute Series (Kluwer Academic, Dordrecht, The Netherlands, 1993), pp. 157–178.
  11. J. P. Fillard, Near-Field Optics and Nanoscopy (World Scientific, Singapore, 1996).
  12. M. A. Paesler, P. J. Moyer, Near-Field Optics (Wiley, New York, 1996).
  13. P. Dawson, K. W. Smith, F. de Fornel, J.-P. Goudonnet, “Imaging of surface plasmon launch and propagation using a photon scanning tunneling microscope,” Ultramicroscopy 57, 287–292 (1995). [CrossRef]
  14. B. Hecht, L. Novotny, H. Bielefeldt, Y. Inouye, D. W. Pohl, “Local excitation, scattering, and interferences of surface plasmons,” Phys. Rev. Lett. 77, 1889–1892 (1996). [CrossRef] [PubMed]
  15. D. Van Labeke, F. I. Baida, J. M. Vigoureux, “A theoretical study of near-field detection and excitation of surface plasmons,” Ultramicroscopy 71, 351–359 (1998). [CrossRef]
  16. A. Madrazo, M. Nieto-Vesperinas, “Detection of subwavelength Goos–Hanchen shifts from near-field intensities: a numerical simulation,” Opt. Lett. 20, 2445–2447 (1995). [CrossRef]
  17. O. Costa de Beauregard, C. Imbert, “Quantized longitudinal and transverse shifts associated with total internal reflection,” Phys. Rev. D 7, 3555–3563 (1973). [CrossRef]
  18. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D 5, 787–796 (1972). [CrossRef]
  19. O. Costa de Beauregard, C. Imbert, Y. Levy, “Observation of shifts in total reflection of a light beam by a multilayered structure,” Phys. Rev. D 15, 3553–3562 (1977). [CrossRef]
  20. C. C. Chan, T. Tamir, “Angular shift of a Gaussian beam reflected near the Brewster angle,” Opt. Lett. 10, 378–380 (1985). [CrossRef] [PubMed]
  21. T. Tamir, “Nonspecular phenomena in beam fields reflected by multilayered media,” J. Opt. Soc. Am. A 3, 558–565 (1986). [CrossRef]
  22. C. C. Chan, T. Tamir, “Beam phenomena at and near critical incidence upon a dielectric interface,” J. Opt. Soc. Am. A 4, 655–663 (1987). [CrossRef]
  23. W. Nasalski, T. Tamir, L. Lin, “Displacement of the intensity peak in narrow beams reflected at a dielectric interface,” J. Opt. Soc. Am. A 5, 132–140 (1988). [CrossRef]
  24. W. Nasalski, “Modified reflectance and geometrical deformations of Gaussian beams reflected at a dielectric interface,” J. Opt. Soc. Am. A 6, 1447–1454 (1989). [CrossRef]
  25. F. Falco, T. Tamir, “Improved analysis of nonspecular phenomena in beams reflected from stratified media,” J. Opt. Soc. Am. A 7, 185–190 (1990). [CrossRef]
  26. R. A. Depine, N. E. Bonomo, “Spatial modifications of Gaussian beams reflected at anisotropic–uniaxial interfaces,” J. Mod. Opt. 42, 2401–2412 (1995). [CrossRef]
  27. N. Bonomo, R. A. Depine, “Nonspecular reflection of ordinary and extraordinary beams in uniaxial media,” J. Opt. Soc. Am. A 14, 3402–3409 (1997). [CrossRef]
  28. G. Y. Leng, D. F. Gu, X. Y. Zang, “Nonspecular longitudinal shift of the beam reflected from an interface containing an absorbing medium,” Opt. Eng. 33, 2612–2616 (1994). [CrossRef]
  29. J. J. Greffet, M. Nieto-Vesperinas, “Field theory for generalized bidirectional reflectivity: derivation of Helmholtz’s reciprocity principle and Kirchhoff’s law,” J. Opt. Soc. Am. A 15, 2735–2744 (1998). [CrossRef]
  30. D. Courjon, K. Sarayeddine, M. Spajer, “Scanning tunneling optical microscopy,” Opt. Commun. 71, 23–28 (1989). [CrossRef]
  31. F. L. Pedrotti, L. S. Pedrotti, Introduction to Optics, 2nd ed. (Prentice Hall, London, 1993), Chap. 22.
  32. B. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), Chap. 3.
  33. Y. Fainman, J. Shamir, “Polarization of nonplanar wave fronts,” Appl. Opt. 23, 3188–3195 (1984). [CrossRef] [PubMed]
  34. F. Y. Kou, T. Tamir, “Range extension of surface plasmons by dielectric layers,” Opt. Lett. 12, 367–369 (1987). [CrossRef] [PubMed]
  35. F. Y. Kou, T. Tamir, “Incidence angles for optimized ATR excitation of surface plasmons,” Appl. Opt. 27, 4098–4103 (1988). [CrossRef] [PubMed]
  36. E. F. Y. Kou, T. Tamir, “Excitation of surface plasmons by finite width beams,” Appl. Opt. 28, 1169–1177 (1989). [CrossRef] [PubMed]
  37. Z. Bouchal, M. Olivik, “Non-diffractive vector Bessel beams,” J. Mod. Opt. 42, 1555–1566 (1995). [CrossRef]
  38. R. Simon, E. C. G. Sudarshan, M. Mukunda, “Gaussian–Maxwell beams,” J. Opt. Soc. Am. A 3, 536–540 (1986). [CrossRef]
  39. D. Hall, “Vector beam solutions of Maxwell’s wave equation,” Opt. Lett. 21, 9–11 (1996). [CrossRef] [PubMed]
  40. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991), Chap. 2.
  41. J. P. Hugonin, R. Petit, “Etude générale des déplacements à la réflexion totale,” J. Opt. (Paris) 8, 73–87 (1977). [CrossRef]
  42. J. J. Greffet, C. Baylard, “Nonspecular astigmatic reflection of a 3D Gaussian beam on an interface,” Opt. Commun. 93, 271–276 (1992). [CrossRef]
  43. J. J. Greffet, C. Baylard, “Nonspecular reflection from a lossy dielectric,” Opt. Lett. 18, 1129–1131 (1993). [CrossRef] [PubMed]
  44. J. Lekner, Theory of Reflection of Electromagnetic and Particle Waves (Nijhoff, Dordrecht, The Netherlands, 1987).
  45. J. M. Vigoureux, “Use of Einstein’s addition law in studies of reflection by stratified planar structures,” J. Opt. Soc. Am. A 9, 1313–1319 (1992). [CrossRef]
  46. B. R. Horowitz, T. Tamir, “Lateral displacement of light beam at a dielectric interface,” J. Opt. Soc. Am. 61, 586–594 (1971). [CrossRef]
  47. D. Van Labeke, D. Barchiesi, “Scanning-tunneling optical microscopy: a theoretical macroscopic approach,” J. Opt. Soc. Am. A 9, 732–738 (1992). [CrossRef]
  48. D. Van Labeke, D. Barchiesi, “Probes for scanning tunneling optical microscopy: a theoretical comparison,” J. Opt. Soc. Am. A 10, 2193–2201 (1993). [CrossRef]

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