Abstract

Scanning Near-field Optical Microscopies suffer from the low signal to noise ratio, due to the smallness of the diffracting probe used to get images. Therefore a lock-in amplifier is commonly used to perform homodyne detection. From the lock-in data, we reconstruct the near-field intensity diffracted by the probe-end in the case of approach curves. We show that the reconstructed and the detected signals can strongly differ. The reconstruction of the signal is necessary to give physical interpretation.

© 2005 Optical Society of America

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References

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J. Appl. Phys. (1)

J.N. Walford, J.A. Porto, R. Carminati, J.J. Greffet, P.M. Adam, S. Hudlet, J.L. Bijeon, A. Stashkevitch, and P. Royer, �??Influence of tip modulation on image formation in scanning near-field optical microscopy,�?? J. Appl. Phys. 89, 5159-5169 (2001).
[CrossRef]

J. Chem. Phys. (1)

A. Dereux, C. Girard, and J.C. Weeber, �??Theoretical principles of near-field optical microscopies and spectroscopies,�?? J. Chem. Phys. 112, 7775-7789 (2000).
[CrossRef]

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

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

Opt. Commun. (1)

R. Fikri, T. Grosges, and D. Barchiesi, �??Apertureless scanning near-field optical microscopy: Numerical modeling of the lock-in detection,�?? Opt. Commun. 232, 15-23 (2004).
[CrossRef]

Opt. Lett. (1)

Prog. Surf. Sci. (1)

J.J. Greffet and R. Carminati, �??Image formation in near-field optics,�?? Prog. Surf. Sci. 56, 133-237 (1997).
[CrossRef]

Rep. Prog. Phys. (2)

C. Girard, C. Joachim, and S. Gauthier, �??The physics of the near-field,�?? Rep. Prog. Phys. 63, 893-938 (2000).
[CrossRef]

D. Courjon and C. Bainier, �??Near field microscopy and near field optics,�?? Rep. Prog. Phys. 57, 989-1027 (1994).
[CrossRef]

Other (2)

I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products. (Academic Press Inc., London, 1994).

M. Born, E. Wolf, Principle of Optics (Pergamon Press, Oxford, 1993).

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Figures (6)

Fig. 1.
Fig. 1.

(a) Schematic of the “ideal” ASNOM experimental setup without lock-in detection. The corresponding ideal signal si (z 0) is the near-field data of interest. (b) Schematic of the ASNOM experimental setup with lock-in detection, used to increase the signal to noise ratio. The recorded data are Fourier harmonics of the near-field signal H 1, …, HN .

Fig. 2.
Fig. 2.

Influence of the amplitude of vibration A(z 0) on the first harmonic |H 1| and the ideal signal si (z 0).

Fig. 3.
Fig. 3.

Reconstitution of the approach curve in the case of an evanescent field. The ideal si (z 0) and the detected |H 1| signals are plotted with plus and star symbols, respectively.

Fig. 4.
Fig. 4.

Approach curves map on a period of the fringes: ϕ ∈ [0,180°]. The maps |H 1| and Si correspond respectively to the first harmonic and to the ideal signal.

Fig. 5.
Fig. 5.

Ideal signal and simulation of the first harmonic amplitude given by the lock-in amplifier for various amplitudes of vibration A for ϕ = 0 (a) and ϕ = π (c). Ideal signal and simulation of the reconstructed signal from the first harmonics for various amplitudes of vibration A for ϕ= 0 (b) and ϕ=π(d).

Fig. 6.
Fig. 6.

Computed first harmonic of the detected signal |H 1|, the reconstructed signals R 0(z 0), R 1(z 0) and R 2(z 0) and the ideal signal si (z 0) above (a) a bright fringe (ϕ = 0) and (b) a dark fringe (ϕ = π).

Equations (12)

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H n = f ( 1 f ) s i ( z tip ( t ) ) exp ( jn 2 πft ) dt .
H n = 1 A ( z 0 ) π z 0 A ( z 0 ) z 0 + A ( z 0 ) s i ( z tip ) cos ( n arccos z tip z 0 A ( z 0 ) ) 1 ( z tip z 0 A ( z 0 ) ) 2 d z tip ,
= 1 π 1 + 1 s i ( ζ ) T n ( ζ ) 1 ζ 2 ,
s i ( z 0 + A ( z 0 ) ζ ) = H 0 T 0 ( ζ ) + 2 n = 1 H n T n ( ζ ) .
R N ( z 0 + A ( z 0 ) ζ ) = H 0 T 0 ( ζ ) + 2 n = 1 N H n T n ( ζ ) .
s i ( z 0 + A ( z 0 ) ζ ) = lim N R N ( z 0 + A ( z 0 ) ζ ) .
s i ( z ) = E t exp ( z D p ) 2 .
H n = ( 1 ) n E t 2 exp ( 2 z 0 D p ) I n ( 2 A ( z 0 ) D p ) ,
s i ( z ) = E t exp ( z D p ) + cos ( ϕ ) E g 2 ,
= E t 2 exp ( 2 z D p ) + 2 cos ( ϕ ) E t E g exp ( z D p ) + E g 2 cos 2 ( ϕ ) ,
H n = ( 1 ) n [ E t 2 exp ( 2 z 0 D p ) I n ( 2 A ( z 0 ) D p )
+ 2 E t E g cos ( ϕ ) exp ( z 0 D p ) I n ( A ( z 0 ) D p ) + E g 2 cos 2 ( ϕ ) δ n 0 ] ,

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