Abstract

We describe the reflection of a strongly focused beam from an interface between two dielectric media. If the beam is incident from the optically denser medium, the image generated by the reflected light is strongly aberrated. This situation is encountered in high-resolution confocal microscopy and data sampling based on solid immersion lenses and oil immersion objectives. The origin of the observed aberrations lies in the nature of total internal reflection, for which there is a phase shift between incident and reflected waves. This phase shift displaces the apparent reflection point beyond the interface, similarly to the Goos–Hänchen shift.

© 2001 Optical Society of America

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References

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  1. K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
    [CrossRef]
  2. H. Maeckler and G. Lehmann, Ann. Phys. (Leipzig) 10, 115, 153 (1952).
  3. G. Lehmann and H. Maeckler, Ann. Phys. (Leipzig) 10, 161 (1952).
    [CrossRef]
  4. T. D. Milster, J. S. Jo, and K. Hirota, Appl. Opt. 38, 5046 (1999).
    [CrossRef]
  5. B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
    [CrossRef]
  6. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
    [CrossRef]
  7. B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
    [CrossRef]

2000 (2)

K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
[CrossRef]

B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef]

1999 (1)

1959 (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

1952 (2)

H. Maeckler and G. Lehmann, Ann. Phys. (Leipzig) 10, 115, 153 (1952).

G. Lehmann and H. Maeckler, Ann. Phys. (Leipzig) 10, 161 (1952).
[CrossRef]

Hecht, B.

B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef]

Hirota, K.

Jo, J. S.

Karrai, K.

K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
[CrossRef]

Lehmann, G.

H. Maeckler and G. Lehmann, Ann. Phys. (Leipzig) 10, 115, 153 (1952).

G. Lehmann and H. Maeckler, Ann. Phys. (Leipzig) 10, 161 (1952).
[CrossRef]

Lorenz, X.

K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
[CrossRef]

Maeckler, H.

H. Maeckler and G. Lehmann, Ann. Phys. (Leipzig) 10, 115, 153 (1952).

G. Lehmann and H. Maeckler, Ann. Phys. (Leipzig) 10, 161 (1952).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Milster, T. D.

Novotny, L.

K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
[CrossRef]

B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Sick, B.

B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef]

Wolf, E.

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

Ann. Phys. (Leipzig) (2)

H. Maeckler and G. Lehmann, Ann. Phys. (Leipzig) 10, 115, 153 (1952).

G. Lehmann and H. Maeckler, Ann. Phys. (Leipzig) 10, 161 (1952).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Karrai, X. Lorenz, and L. Novotny, Appl. Phys. Lett. 77, 3459 (2000).
[CrossRef]

Phys. Rev. Lett. (1)

B. Hecht, B. Sick, and L. Novotny, Phys. Rev. Lett. 85, 4482 (2000).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

B. Richards and E. Wolf, Proc. R. Soc. London Ser. A 253, 358 (1959).
[CrossRef]

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, New York, 1995).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

A linearly polarized beam is reflected by a beam splitter (BS) and focused by a high-NA objective lens with focal radius f onto an interface between two dielectric media, n 1 and n 2 . The reflected field is collected by the same lens, transmitted through the beam splitter, and refocused by a second lens with focal radius f onto the image plane.

Fig. 2
Fig. 2

Reflected images of a diffraction-limited focused spot. The spot is moved in steps of λ / 4 across the interface. z o is positive (negative) when the focus is below (above) the interface. Upper row, glass–air interface n 2 = 1 ; lower row, glass–metal interface ϵ 2 - . The arrow indicates the direction of polarization of the incoming beam. Image size, 4.75 M λ .

Fig. 3
Fig. 3

Decomposition of the in-focus reflected image (upper center image of Fig.  2) into two orthogonal polarizations: (a), (c) polarization in the direction of the incident polarization x ^ : (b), (d) polarization perpendicular to the incident polarization y ^ . (a), (b) Calculated patterns, (c), (d) experimental patterns. Image size, 4.75 M λ .

Equations (8)

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E r = 1 2 π k x , k y E ^ k x , k y exp i k · r d k x d k y .
E ^ k x , k y = if exp - ik 1 r k z 1 E k x , k y , k z 1 ,
E ref r = - ifE o exp - ik 1 f 2 π k 1 2 n o n 1 × k x , k y exp i k x x + k y y - k z 1 z - 2 z o × [ k x 2 k z 1 r p - k y 2 k 1 r s k x k y k z 1 r p + k 1 r s k x k x 2 + k y 2 r p ] k 1 / k z 1 k x 2 + k y 2 d k x d k y .
E ref = - E o exp 2 ik 1 1 - f / ρ 2 1 / 2 z o cos 2 ϕ r p ρ - sin 2 ϕ r s ρ x ^ + 1 2 sin 2 ϕ r p ρ + r s ρ y ^ ,
k z 3 = k 3 1 - f 2 f 2 sin 2 θ 1 2 k 3 - k 3 2 f 2 f 2   sin 2 θ ,
E ref ρ , φ , z = E o k 3 f 2 2 if exp - ik 3 z + f × I 0 + I 2 cos 2 φ x ^ - I 2 sin 2 φ y ^ n o n 3 ,
I 0 ρ , z = 0 θ max cos θ sin θ r p θ - r s θ × J 0 k 3 ρ sin θ f / f × exp i / 2 k 3 z f / f 2   sin 2 θ + 2 ik 1 z o cos θ ] d θ ,
I 2 ρ , z = 0 θ max cos θ sin θ r p θ + r s θ × J 2 k 3 ρ sin θ f / f × exp i / 2 k 3 z f / f 2   sin 2 θ + 2 ik 1 z o cos θ ] d θ .

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