Abstract

Conditions for the production of near-circular polarization states of the evanescent field present in the rarer medium in total internal reflection of incident monochromatic p-polarized light at a dielectric– dielectric planar interface are determined. Such conditions are satisfied if high-index (>3.2) transparent prism materials (e.g., GaP and Ge) are used at angles of incidence well above the critical angle but sufficiently below grazing incidence. Furthermore, elliptical polarization of incident light with nonzero p and s components can be tailored to cause circular polarization of the resultant tangential electric field in the plane of the interface or circular polarization of the transverse electric field in a plane normal to the direction of propagation of the evanescent wave. Such polarization control of the evanescent field is significant, e.g., in the fluorescent excitation of molecules adsorbed at solid–liquid and solid–gas interfaces by total internal reflection.

© 2011 Optical Society of America

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References

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  1. F. de Fornel, Evanescent Waves (Springer, 2001).
  2. L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge, 2006).
  3. L. Józefowski, J. Fiutowski, T. Kawalec, and H.-G. Rubahn, “Direct measurement of the evanescent-wave polarization state,” J. Opt. Soc. Am. B 24, 624–628 (2007).
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  4. A. Norrman, T. Setälä, and A. T. Friberg, “Partial coherence and partial polarization in random evanescent fields on lossless interfaces,” J. Opt. Soc. Am. A 28, 391–400 (2011).
    [CrossRef]
  5. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]
  6. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).
  7. R. M. A. Azzam, “Phase shifts that accompany total internal reflection at a dielectric-dielectric interface,” J. Opt. Soc. Am. A 21, 1559–1563 (2004).
    [CrossRef]
  8. E. H. Hellen, R. M. Fulbright, and D. Axelrod, “Total internal reflection fluorescence theory and applications at biosurfaces,” in Spectroscopic Membrane Probes, L.M.Loew, ed. (CRC Press, 1988), Vol. II, pp. 47–79.
  9. K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.
    [CrossRef]
  10. S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
    [CrossRef] [PubMed]
  11. A. Borghesi and G. Guizzetti, “Gallium phosphide,” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 445–464.
  12. W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. I, Chap. 33.
  13. J. Michl and E. W. Thulstrup, Spectroscopy with Polarized Light (VCH, 1995).

2011 (1)

2007 (1)

2004 (1)

1999 (1)

S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
[CrossRef] [PubMed]

1969 (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Axelrod, D.

S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
[CrossRef] [PubMed]

E. H. Hellen, R. M. Fulbright, and D. Axelrod, “Total internal reflection fluorescence theory and applications at biosurfaces,” in Spectroscopic Membrane Probes, L.M.Loew, ed. (CRC Press, 1988), Vol. II, pp. 47–79.

Azzam, R. M. A.

Bashara, N. M.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

Borghesi, A.

A. Borghesi and G. Guizzetti, “Gallium phosphide,” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 445–464.

de Fornel, F.

F. de Fornel, Evanescent Waves (Springer, 2001).

Drexhage, K. H.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.
[CrossRef]

Fiutowski, J.

Friberg, A. T.

Fulbright, R. M.

E. H. Hellen, R. M. Fulbright, and D. Axelrod, “Total internal reflection fluorescence theory and applications at biosurfaces,” in Spectroscopic Membrane Probes, L.M.Loew, ed. (CRC Press, 1988), Vol. II, pp. 47–79.

Guizzetti, G.

A. Borghesi and G. Guizzetti, “Gallium phosphide,” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 445–464.

Harris, T. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. I, Chap. 33.

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge, 2006).

Hellen, E. H.

E. H. Hellen, R. M. Fulbright, and D. Axelrod, “Total internal reflection fluorescence theory and applications at biosurfaces,” in Spectroscopic Membrane Probes, L.M.Loew, ed. (CRC Press, 1988), Vol. II, pp. 47–79.

Józefowski, L.

Kawalec, T.

Michl, J.

J. Michl and E. W. Thulstrup, Spectroscopy with Polarized Light (VCH, 1995).

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Norrman, A.

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge, 2006).

Rubahn, H.-G.

Setälä, T.

Sund, S. E.

S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
[CrossRef] [PubMed]

Swanson, J. A.

S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
[CrossRef] [PubMed]

Thomas, M. E.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. I, Chap. 33.

Thulstrup, E. W.

J. Michl and E. W. Thulstrup, Spectroscopy with Polarized Light (VCH, 1995).

Tropf, W. J.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. I, Chap. 33.

Biophys. J. (1)

S. E. Sund, J. A. Swanson, and D. Axelrod, “Cell membrane orientation visualized by polarized total internal reflection fluorescence,” Biophys. J. 77, 2266–2283 (1999).
[CrossRef] [PubMed]

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

J. Opt. Soc. Am. B (1)

Surf. Sci. (1)

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Other (8)

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, 1987).

A. Borghesi and G. Guizzetti, “Gallium phosphide,” in Handbook of Optical Constants of Solids, E.D.Palik, ed. (Academic, 1985), pp. 445–464.

W. J. Tropf, M. E. Thomas, and T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M.Bass, ed. (McGraw-Hill, 1995), Vol. I, Chap. 33.

J. Michl and E. W. Thulstrup, Spectroscopy with Polarized Light (VCH, 1995).

F. de Fornel, Evanescent Waves (Springer, 2001).

L. Novotny and B. Hecht, Principles of Nano-Optics(Cambridge, 2006).

E. H. Hellen, R. M. Fulbright, and D. Axelrod, “Total internal reflection fluorescence theory and applications at biosurfaces,” in Spectroscopic Membrane Probes, L.M.Loew, ed. (CRC Press, 1988), Vol. II, pp. 47–79.

K. H. Drexhage, “Interaction of light with monomolecular dye layers,” in Progress in Optics, E.Wolf, ed. (Elsevier, 1974), Vol. 12, pp. 163–232.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Total internal reflection of p- and s-polarized light at a dielectric–dielectric interface at angle of incidence ϕ and the reference x y z coordinate system used to describe the incident and evanescent refracted wave fields.

Fig. 2
Fig. 2

Circular polarization state (CS, e = 1 ) and an elliptical near-circular state (ENCS) with e = b / a = 0.95 .

Fig. 3
Fig. 3

Ellipticity e = b / a of the evanescent electric field [Eq. (10)] is plotted as a function of ϕ from the critical angle to grazing incidence at constant values of N from 2 to 6 in steps of 1.

Fig. 4
Fig. 4

Amplitude ratio | χ i | = E i s / E i p [Eq. (18)] required to produce circular polarization of the tangential electric field in the plane of the interface is plotted as a function of ϕ from the critical angle to grazing incidence for constant values of N from 2 to 6 in steps of 1.

Fig. 5
Fig. 5

Amplitude ratio | χ i | = E i s / E i p for circular polarization of the tangential electric field at ϕ = 90 ° and ϕ m = arcsin 2 / ( N 2 + 1 ) [Eqs. (20, 21)] is plotted versus N in the range 2 N 6 .

Fig. 6
Fig. 6

Phase difference δ i s δ i p [Eq. (19)] between the incident s and p components of incident light, which is required to produce circular polarization of the tangential electric field, is plotted as a function of ϕ from the critical angle to grazing incidence for constant N values from 2 to 6 in steps of 1.

Fig. 7
Fig. 7

Amplitude ratio | χ i | = E i s / E i p [Eq. (24)], which is required to produce circular polarization of the transverse electric field of the evanescent wave, is plotted as a function of ϕ from the critical angle to grazing incidence for N values from 2 to 6 in steps of 1.

Equations (33)

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E i = [ E i x E i y E i z ] t = [ ( sin ϕ ) E i p E i s ( cos ϕ ) E i p ] t ,
E e = [ E e x E e y E e z ] t ,
E e x = T 11 E i x , E e y = T 22 E i y , E e z = T 33 E i z ,
T 11 = N 2 ( 1 + r p ) , T 22 = ( 1 + r s ) , T 33 = ( 1 r p ) .
r p = exp ( j δ p ) , r s = exp ( j δ s ) .
tan ( δ p / 2 ) = N sec ϕ ( N 2 sin 2 ϕ 1 ) 1 / 2 , tan ( δ s / 2 ) = N 1 sec ϕ ( N 2 sin 2 ϕ 1 ) 1 / 2 .
χ e = E e z / E e x .
χ e = ( cot ϕ / N 2 ) [ ( r p 1 ) / ( r p + 1 ) ]
χ e = ( cot ϕ / N 2 ) [ j tan ( δ p / 2 ) ] .
χ e = j b / a = j e = j [ 1 ( csc ϕ / N ) 2 ] 1 / 2 .
e max = [ 1 ( 1 / N ) 2 ] 1 / 2 = cos ϕ c
N = 1 / 1 e max 2 .
χ i = E i s / E i p ,
χ e t = E e z / E e y .
χ e t = ( cos ϕ / χ i ) [ ( r p 1 ) / ( r s + 1 ) ] .
χ e t = ± j .
χ i = E i s / E i p = cos ϕ [ sin ( δ p / 2 ) / cos ( δ s / 2 ) ] exp [ j ( δ p δ s ) / 2 ] .
| χ i | = | E i s | / | E i p | = ( N 2 sin 2 ϕ 1 ) 1 / 2 / [ ( N 2 + 1 ) sin 2 ϕ 1 ] 1 / 2 ,
δ i s δ i p = arctan [ ( N 2 sin 2 ϕ 1 ) 1 / 2 / ( N sin ϕ tan ϕ ) ] .
| χ i | 90 = ( N 2 1 ) 1 / 2 / N .
| χ i | = ( N 2 1 ) 1 / 2 / ( N 2 + 1 ) 1 / 2 .
χ e T = E e y / E e x .
χ i = χ e T ( N 2 sin ϕ ) [ ( r p + 1 ) / ( r s + 1 ) ] .
| χ i | = | E i s | / | E i p | = ( N sin ϕ ) / [ ( N 2 + 1 ) sin 2 ϕ 1 ] 1 / 2 ,
δ i s δ i p = arctan [ ( N 2 sin 2 ϕ 1 ) 1 / 2 / ( N sin ϕ tan ϕ ) ] + π / 2.
k e = j k e x x ^ + k e z z ^ ,
k e z = k i z = ( 2 π n 0 / λ ) sin ϕ ,
k e · k e = ( 2 π n 1 / λ ) 2 = k e z 2 k e x 2 .
k e x = ( 2 π n 1 / λ ) ( N 2 sin 2 ϕ 1 ) 1 / 2
E e ( x , y , z ) = [ E e x 0 E e z ] t exp ( k e x x ) exp ( j k e z z ) .
· E e = 0.
χ e = E e z / E e x = j k e x / k e z .
χ e = j [ 1 ( csc ϕ / N ) 2 ] 1 / 2 ,

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