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Seeing inside a Fabry-Pérot resonator by means of a scanning tunneling optical microscope
1 August 1994
OPTICS COMMUNICATIONS Optics Communications 110 (1994) 7-12
ELSEVIER
Seeing inside a Fabry-Pkrot resonator by means of a scanning tunneling optical microscope D. Courjon, C. Bainier, F. Baida Laboratoire d’optique P.M. Duffieux, VRA 214 CNRS, Vniversitk de Franche-ComtP, VFR Sciences, 25030 Besancon cedex, France
Received 24 January 1994
Abstract By integrating a scanning tunneling optical microscope inside a Fabry-Perot resonator, it is possible to map very precisely the structure of the electromagnetic field inside the resonant cavity. Moreover, by working in antiresonant mode (dark field conditions), it is possible to locally remove the incident evanescent field. This particular configuration increases the z-resolution in such microscopes.
1. Introduction In near field microscopy emphasis is generally put on the subwavelength resolution that can be reached. The scanning tunneling optical microscopy (STOM) [ 1,2 ] offers an interesting feature, i.e., the ability to detect evanescent fields in guiding structures [ 3,4] without significantly perturbing the guiding system. It is thus possible to follow the propagation of a guided beam inside an optical integrated circuit by analyzing the evanescent field outside the structure. Based on the same idea, recent attempts have demonstrated the possibility of imaging very simply and clearly localized plasmons over a surface [ 5 1. Following the same principle, here we analyze the propagation of a light beam inside a Fabry-Perot interferometer, by combining it with a scanning tunneling optical microscope (see Fig. 1). The evanescent field over the prism surface will be then composed of the superposition of a number of plane non homogeneous waves. This superposition leads to a standing evanescent field whose structure will be described in the theoretical part. Finally, scanning the 0030-4018/94/$07.00
M (r,,
Fig. 1. Schematic of the set-up
evanescent field with a thin dielectric tip will be strictly equivalent to exploring the field inside the Fabry-Perot. Let us note that the principle of generating interference between evanescent waves is not new [ 6,7]. However, as shown in the Refs. [ 8,9], scanning tunneling optical microscopy is probably the best tool to
0 1994 Elsevier Science B.V. All rights reserved
SSDI0030-4018(94)00236-N
D. Courjon et al. /Optics Communications 1 IO (1994) 7- 12
8
map the structure of the resulting evanescent field with precision. In our case, the prism is used to fold the beam in order to generate the non-homogeneous light waves. The light beam inside the prism is reflected between the mirror M and the beamsplitter BS. The field is then picked up by means of a tapered fiber exploring the field above the surface.
2. Theory
For the sake of simplicity, we assume that the tip is so small that there is no interaction between tip and sample (dipolar approximation). Beamsplitter, mirror and prism surfaces are characterized by the reflection and transmission factors, ri, t,, r2, t2, r, t, respectively. The modeling is based on the resolution of Maxwell equations by ensuring continuity conditions for the electric and magnetic fields on the boundaries. The incident wave is a plane wave characterized by its k-vector and by its polarization. A straightforward calculation leads to the following expression for the electric field at a given point A (x, y, z) above the prism: E(x, Y, z) =&t,
exp( -Gh 1
x{exp[i(K,x+K,y+K,z)l +r,rexp[
3. Simulation For carrying out the simulation, we first needed to determine experimentally the value of the coeffcients r,, t,, r2, of the beamsplitter and of the mirror. Moreover, we have assumed that the metal coating of these two components is perfectly conducting. Fig. 2 represents the distribution of the light intensity on the surface of the prism along the x-direction, for a TE polarization incident light beam (a) and for the TM polarization (b). The period of the interference pattern is equal to J/2n sin( 0) (where n is the refractive index of the prism and B is the angle of incidence). If we move the beamsplitter along the udirection, the sinusoidal pattern remains but the amplitude of the fringes varies (see Figs. 2c, d). The shift observed between TM and TE modes is due to the difference of phase at the total reflection between the two polarization modes. Now, if we analyze the intensity variations at a fixed point located above the prism versus the mirror position (in the &direction), the resulting plotted intensity curve looks like that of conventional FabryPerot interferometers (see Fig. 3a, in TE polarization ). According to the parameters in Eq. ( 1)) we can note symmetrical or asymmetrical peak shape. The distance between two resonance peaks equals J.12. The second polarization mode TM is shown in Fig. 3b. As for the TE polarization, the overall shape reminds the Fabry-Perot output intensity distribution. If the field is composed of the mixture of the two polarizations, we observe the existence of two peaks well differen-
-i(K,x+K,y-K,z+2@,)]}
X{l-r2r,r,exp[-2i(@,+@,)]}-‘,
(1)
where 9, = (2n/L)e,, @2= (2n/A)e2, and K,, K, and K, are the components of the wave vector above the prism. We note that the field expression is composed of two terms. The first one is the well-known field distribution in the output plane of a Fabry-Perot interferometer, whereas the second one is due to the asymmetry between the two arms of the interferometer. The coefficients r and t are determined from the Fresnel formulas in the case of total internal reflection.
0 0
100
200
300
400
500
600
700
x(nm)
Fig. 2. Plotted intensity distributions above the prism surface, along the x-direction (zA= 1 nm); (a, c) and (b, d) correspond to TE and TM modes respectively, for two beamsplitter positions.
9
D. Courjon et al. /Optics Communications110 (1994) 7-12 16
fiM = 2 arctan
14 12 3
6
I
4
ncos(8)
>.
(2)
For 8= 45 degrees and n = 1.5 15 the phase difference v/= 1PTE- c/+M1is about 39 degrees. It corresponds to a shift of the mirror of about 69 nm.
10
s. 8
-
CJ
n2 sin’ (8) - 1
i \
0
100
200
300
e2
400
J \+
4. Experiment
500
600
700
500
600
700
The experimental setup is described in Fig. 4. As previously mentioned, it is a conventional STOM placed inside a Fabry-Perot interferometer. The prism is BK7 and the two right faces are coated in order to limit parasitic reflections. The aluminum mirror M can be shifted along its optical axis by means of a piezo transducer corrected from hysteresis. The motion of M can be set manually or by computer control. The reflection coefficients (in energy) of the semi-transparent plate BS and of the mirror M are 70% and 92%, respectively. The tip used as a collector is a tapered optical fiber, the fabrication of which has been described in several papers. The signal is then transmitted to a cooled photomultiplier. In order to increase the signal to noise ratio, the laser beam (HeNe laser) is modulated at 10 kHz and the signal is detected by means of a lock-in amplifier (synchronous detection).
(nm)
80 70 60
-0
100
200
300
400
e2 (nm) 4 3.5 3 7 2.5 zi 2 - 1.5 1
5. Results
0.5 0 0
100
200
300
400
500
600
700
e2 (4 Fig. 3. Plotted intensity curves versus the mirror position at a given point above the prism; 3 (a) and (b ) correspond to TE and TM modes respectively, (c) corresponds to a mixture of TE and TM (zA= 1 nm).
tiated, due to the differences of phases between and TM modes (Fig. 3~). The phases V)TEand qT&, at the total reflection TE and TM modes take the form:
a)rE = 2 arctan
TE for
First, the prism surface is scanned along the F-direction in constant altitude mode. The experimental intensity detected by the tip is shown in Fig. 5. The field, as predicted by the theory, is quite sinusoidal. The period is in good agreement with the predicted value. The second series of recordings has been carried out by bringing the tip near the surface and by moving the mirror M. The curves representing the intensity variations are shown in Figs. 6a, b, c. Asymmetrical and symmetrical shapes can be obtained depending on the experimental settings (see Fig. 6a and Fig. 6b). As predicted by the theory, we observed a shift of about 70 nanometers when rotating the polarization from TE to TM. In the case of TE
10
D. Courjon et al. / Optics Communications I10 (1994) 7- I2
x,y,z PZT actuator
intensity
modulator
I
I
Fig. 4. Experimental set-up. The source is a HeNe laser of 10 mW, ensuring a temporal coherence length better than 50 cm. The acoustic cell modulates the laser beam at a frequency of 10 kHz. The oiezo actuator attached to the prism is an inchworm positioner allowing both precise and large scale.
.
tf0
100
';j-:
200
300 400 x (nm)
500
600
700
Fig. 5. Experimental recording of the detected intensity by scanning the prism surface at a few nanometers from the surface along the x-axis. To be compared with Fig. 2.
and TM mixture, we note two peaks corresponding to the two polarizations states (see Fig. 6~). This phase shift is responsible for the Goos-Hanchen shift
[lOIThese first results shows the possibility to discriminate the two polarization modes by simply moving the mirror along the u-axis. Since the finesse of the
interferometer only depends on the reflection coefticient of the cavity and on the tip size, we can imagine a new high resolution local spectroscopy, i.e., the transposition in the near field of the Fabry-Perot spectroscopy [ 111. Finally, such a technique allows one to follow the field inside the resonator without perturbing the field too much: although the theoretical development assumes no interaction with the tip, the agreement with experiment is good. Finally, it allows one to give a precise and faithful description of the temporal behavior of the field enclosed between the two reflectors. Among the possible applications in microscopy, one should be the possibility of working in antiresonant mode, that is in choosing a mirror position corresponding to a minimum of intensity in the evanescent field. By working in such a configuration, i.e., in dark field conditions, first, we could dramatically limit the stray light entering the walls of the fiber and second we could only detect the signal due to the coupling between tip and sample by avoiding detection of the incident evanescent field. The first attempts confirming these speculations are shown in Fig. 7. The
11
D. Courjonetal. /OpticsCommunications llO(1994) 7-12
I
\
\
I J
0
100 200
300 400
\
500 600
700
0
100
200
300
400
500
Z (nrt-0 Fig. 7. Experimental decay versus the distance tip-sample; in (a) STOM configuration, in (b ) antiresonant configuration. The two curves have been normaiized. The actual maximum intensity in STOM configuration is 15 times larger than in antiresonant conditions. 0
100 200
300 400 500 e, (nm)
600
700
ods is obviously (x) resolutions.
to increase both axial (z) and lateral
6. Conclusion
I 2
J!i -
0
100 200
300 400 s (nm)
500 600
700
Fig. 6. Experimental recordings of the intensity variations versus mirror position; 6(a) and (b) show asymmetrical and symmetrical shapes depending on the settings, (c) shows the case of TE and TM mixing. To be compared with Fig. 3c.
curves show the exponential decay of the field intensity at a given point above the object, when removing the tip from the surface, in the classical STOM configuration (a) and in the antiresonant mode (b). We note a reduction of the penetration depth by a factor of about 2.3. This technique could be an alternative to other ways recently developed for reducing the penetration depth [ 121. The interest of such meth-
In this communication, we have shown that the analysis of interfering evanescent fields can provide data that are generally not accessible by conventional detection techniques. Moreover, in the precise case of a Fabry-Perot resonator, by working in antiresonance condition, it should be probably possible to increase significantly both signal to noise ratio and X, z resolution.
References [ 1 ] D. Courjon, K. Sarayeddine and 71 (1989) 23. [2] R.C. Reddick, R.J. Warmack and 39 (1989) 767. [3] K. Sarayeddine, D. Coujon and storage and scanning technology, 68.
M. Spajer, Optics Comm. T.L. Ferrell, Phys. Rev. B M. Spajer, SPIE, Optical Proc. Vol. 1139 ( 1989) p.
D. Courjon et al. / Optics Communications I10 (1994) 7- I2 M. Chudgar, A. Choo, H. Jackson, G. de Brabander, M. Kumar and J. Boyd, Photon scanning tunneling of optical channel waveguides, Second International Conference on Near Field Optics NF02, Raleigh, USA ( 1993). P. Dawson, F. de Fornel and J.P. Goudonnet, Imaging of surface plasmon launch and propagation using a photon scanning tunneling microscope, Second International Conference on Near Field Optics, NF02, Raleigh, USA (1993). [6] 0. Bryngdahl, Appl. Optics 59 (1969) 1645. [7] H. Nassenstein, Phys. Lett. 28 A ( 1968) 249. [ 8] A. Meixner, M. Bopp and G. Tarrach, Direct measurement of standing evanescent waves with a photon scanning tunneling microscope, Appl. Optics, to be published.
[ 91 J. Mertz, M. Hipp, J. Mlynek and 0. Marti, Optical nearfield imaging with a semiconductor probe tip, Appl. Phys. Lett., to be published. [ IO] A. Manallah, Etude du dtcalage longitudinal et du dtcalage transversal d’un faisceau lumineux en reflexion totale: mesure par detection heterodyne, These Sciences pour TIngCnieur, University of Franche-Comte, Besancon, 1988. [ll ] M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1959) p. 332. ]l2 ] D.W. Pohl, D. Courjon, C. Bainier, A. Dereux and H. Heinzelmann, Optical tunneling through adjustable liquid metal gap, Proceedings NATO Vol. 242 ( 1992) p. 46.
OPTICS COMMUNICATIONS Optics Communications 110 (1994) 7-12
ELSEVIER
Seeing inside a Fabry-Pkrot resonator by means of a scanning tunneling optical microscope D. Courjon, C. Bainier, F. Baida Laboratoire d’optique P.M. Duffieux, VRA 214 CNRS, Vniversitk de Franche-ComtP, VFR Sciences, 25030 Besancon cedex, France
Received 24 January 1994
Abstract By integrating a scanning tunneling optical microscope inside a Fabry-Perot resonator, it is possible to map very precisely the structure of the electromagnetic field inside the resonant cavity. Moreover, by working in antiresonant mode (dark field conditions), it is possible to locally remove the incident evanescent field. This particular configuration increases the z-resolution in such microscopes.
1. Introduction In near field microscopy emphasis is generally put on the subwavelength resolution that can be reached. The scanning tunneling optical microscopy (STOM) [ 1,2 ] offers an interesting feature, i.e., the ability to detect evanescent fields in guiding structures [ 3,4] without significantly perturbing the guiding system. It is thus possible to follow the propagation of a guided beam inside an optical integrated circuit by analyzing the evanescent field outside the structure. Based on the same idea, recent attempts have demonstrated the possibility of imaging very simply and clearly localized plasmons over a surface [ 5 1. Following the same principle, here we analyze the propagation of a light beam inside a Fabry-Perot interferometer, by combining it with a scanning tunneling optical microscope (see Fig. 1). The evanescent field over the prism surface will be then composed of the superposition of a number of plane non homogeneous waves. This superposition leads to a standing evanescent field whose structure will be described in the theoretical part. Finally, scanning the 0030-4018/94/$07.00
M (r,,
Fig. 1. Schematic of the set-up
evanescent field with a thin dielectric tip will be strictly equivalent to exploring the field inside the Fabry-Perot. Let us note that the principle of generating interference between evanescent waves is not new [ 6,7]. However, as shown in the Refs. [ 8,9], scanning tunneling optical microscopy is probably the best tool to
0 1994 Elsevier Science B.V. All rights reserved
SSDI0030-4018(94)00236-N
D. Courjon et al. /Optics Communications 1 IO (1994) 7- 12
8
map the structure of the resulting evanescent field with precision. In our case, the prism is used to fold the beam in order to generate the non-homogeneous light waves. The light beam inside the prism is reflected between the mirror M and the beamsplitter BS. The field is then picked up by means of a tapered fiber exploring the field above the surface.
2. Theory
For the sake of simplicity, we assume that the tip is so small that there is no interaction between tip and sample (dipolar approximation). Beamsplitter, mirror and prism surfaces are characterized by the reflection and transmission factors, ri, t,, r2, t2, r, t, respectively. The modeling is based on the resolution of Maxwell equations by ensuring continuity conditions for the electric and magnetic fields on the boundaries. The incident wave is a plane wave characterized by its k-vector and by its polarization. A straightforward calculation leads to the following expression for the electric field at a given point A (x, y, z) above the prism: E(x, Y, z) =&t,
exp( -Gh 1
x{exp[i(K,x+K,y+K,z)l +r,rexp[
3. Simulation For carrying out the simulation, we first needed to determine experimentally the value of the coeffcients r,, t,, r2, of the beamsplitter and of the mirror. Moreover, we have assumed that the metal coating of these two components is perfectly conducting. Fig. 2 represents the distribution of the light intensity on the surface of the prism along the x-direction, for a TE polarization incident light beam (a) and for the TM polarization (b). The period of the interference pattern is equal to J/2n sin( 0) (where n is the refractive index of the prism and B is the angle of incidence). If we move the beamsplitter along the udirection, the sinusoidal pattern remains but the amplitude of the fringes varies (see Figs. 2c, d). The shift observed between TM and TE modes is due to the difference of phase at the total reflection between the two polarization modes. Now, if we analyze the intensity variations at a fixed point located above the prism versus the mirror position (in the &direction), the resulting plotted intensity curve looks like that of conventional FabryPerot interferometers (see Fig. 3a, in TE polarization ). According to the parameters in Eq. ( 1)) we can note symmetrical or asymmetrical peak shape. The distance between two resonance peaks equals J.12. The second polarization mode TM is shown in Fig. 3b. As for the TE polarization, the overall shape reminds the Fabry-Perot output intensity distribution. If the field is composed of the mixture of the two polarizations, we observe the existence of two peaks well differen-
-i(K,x+K,y-K,z+2@,)]}
X{l-r2r,r,exp[-2i(@,+@,)]}-‘,
(1)
where 9, = (2n/L)e,, @2= (2n/A)e2, and K,, K, and K, are the components of the wave vector above the prism. We note that the field expression is composed of two terms. The first one is the well-known field distribution in the output plane of a Fabry-Perot interferometer, whereas the second one is due to the asymmetry between the two arms of the interferometer. The coefficients r and t are determined from the Fresnel formulas in the case of total internal reflection.
0 0
100
200
300
400
500
600
700
x(nm)
Fig. 2. Plotted intensity distributions above the prism surface, along the x-direction (zA= 1 nm); (a, c) and (b, d) correspond to TE and TM modes respectively, for two beamsplitter positions.
9
D. Courjon et al. /Optics Communications110 (1994) 7-12 16
fiM = 2 arctan
14 12 3
6
I
4
ncos(8)
>.
(2)
For 8= 45 degrees and n = 1.5 15 the phase difference v/= 1PTE- c/+M1is about 39 degrees. It corresponds to a shift of the mirror of about 69 nm.
10
s. 8
-
CJ
n2 sin’ (8) - 1
i \
0
100
200
300
e2
400
J \+
4. Experiment
500
600
700
500
600
700
The experimental setup is described in Fig. 4. As previously mentioned, it is a conventional STOM placed inside a Fabry-Perot interferometer. The prism is BK7 and the two right faces are coated in order to limit parasitic reflections. The aluminum mirror M can be shifted along its optical axis by means of a piezo transducer corrected from hysteresis. The motion of M can be set manually or by computer control. The reflection coefficients (in energy) of the semi-transparent plate BS and of the mirror M are 70% and 92%, respectively. The tip used as a collector is a tapered optical fiber, the fabrication of which has been described in several papers. The signal is then transmitted to a cooled photomultiplier. In order to increase the signal to noise ratio, the laser beam (HeNe laser) is modulated at 10 kHz and the signal is detected by means of a lock-in amplifier (synchronous detection).
(nm)
80 70 60
-0
100
200
300
400
e2 (nm) 4 3.5 3 7 2.5 zi 2 - 1.5 1
5. Results
0.5 0 0
100
200
300
400
500
600
700
e2 (4 Fig. 3. Plotted intensity curves versus the mirror position at a given point above the prism; 3 (a) and (b ) correspond to TE and TM modes respectively, (c) corresponds to a mixture of TE and TM (zA= 1 nm).
tiated, due to the differences of phases between and TM modes (Fig. 3~). The phases V)TEand qT&, at the total reflection TE and TM modes take the form:
a)rE = 2 arctan
TE for
First, the prism surface is scanned along the F-direction in constant altitude mode. The experimental intensity detected by the tip is shown in Fig. 5. The field, as predicted by the theory, is quite sinusoidal. The period is in good agreement with the predicted value. The second series of recordings has been carried out by bringing the tip near the surface and by moving the mirror M. The curves representing the intensity variations are shown in Figs. 6a, b, c. Asymmetrical and symmetrical shapes can be obtained depending on the experimental settings (see Fig. 6a and Fig. 6b). As predicted by the theory, we observed a shift of about 70 nanometers when rotating the polarization from TE to TM. In the case of TE
10
D. Courjon et al. / Optics Communications I10 (1994) 7- I2
x,y,z PZT actuator
intensity
modulator
I
I
Fig. 4. Experimental set-up. The source is a HeNe laser of 10 mW, ensuring a temporal coherence length better than 50 cm. The acoustic cell modulates the laser beam at a frequency of 10 kHz. The oiezo actuator attached to the prism is an inchworm positioner allowing both precise and large scale.
.
tf0
100
';j-:
200
300 400 x (nm)
500
600
700
Fig. 5. Experimental recording of the detected intensity by scanning the prism surface at a few nanometers from the surface along the x-axis. To be compared with Fig. 2.
and TM mixture, we note two peaks corresponding to the two polarizations states (see Fig. 6~). This phase shift is responsible for the Goos-Hanchen shift
[lOIThese first results shows the possibility to discriminate the two polarization modes by simply moving the mirror along the u-axis. Since the finesse of the
interferometer only depends on the reflection coefticient of the cavity and on the tip size, we can imagine a new high resolution local spectroscopy, i.e., the transposition in the near field of the Fabry-Perot spectroscopy [ 111. Finally, such a technique allows one to follow the field inside the resonator without perturbing the field too much: although the theoretical development assumes no interaction with the tip, the agreement with experiment is good. Finally, it allows one to give a precise and faithful description of the temporal behavior of the field enclosed between the two reflectors. Among the possible applications in microscopy, one should be the possibility of working in antiresonant mode, that is in choosing a mirror position corresponding to a minimum of intensity in the evanescent field. By working in such a configuration, i.e., in dark field conditions, first, we could dramatically limit the stray light entering the walls of the fiber and second we could only detect the signal due to the coupling between tip and sample by avoiding detection of the incident evanescent field. The first attempts confirming these speculations are shown in Fig. 7. The
11
D. Courjonetal. /OpticsCommunications llO(1994) 7-12
I
\
\
I J
0
100 200
300 400
\
500 600
700
0
100
200
300
400
500
Z (nrt-0 Fig. 7. Experimental decay versus the distance tip-sample; in (a) STOM configuration, in (b ) antiresonant configuration. The two curves have been normaiized. The actual maximum intensity in STOM configuration is 15 times larger than in antiresonant conditions. 0
100 200
300 400 500 e, (nm)
600
700
ods is obviously (x) resolutions.
to increase both axial (z) and lateral
6. Conclusion
I 2
J!i -
0
100 200
300 400 s (nm)
500 600
700
Fig. 6. Experimental recordings of the intensity variations versus mirror position; 6(a) and (b) show asymmetrical and symmetrical shapes depending on the settings, (c) shows the case of TE and TM mixing. To be compared with Fig. 3c.
curves show the exponential decay of the field intensity at a given point above the object, when removing the tip from the surface, in the classical STOM configuration (a) and in the antiresonant mode (b). We note a reduction of the penetration depth by a factor of about 2.3. This technique could be an alternative to other ways recently developed for reducing the penetration depth [ 121. The interest of such meth-
In this communication, we have shown that the analysis of interfering evanescent fields can provide data that are generally not accessible by conventional detection techniques. Moreover, in the precise case of a Fabry-Perot resonator, by working in antiresonance condition, it should be probably possible to increase significantly both signal to noise ratio and X, z resolution.
References [ 1 ] D. Courjon, K. Sarayeddine and 71 (1989) 23. [2] R.C. Reddick, R.J. Warmack and 39 (1989) 767. [3] K. Sarayeddine, D. Coujon and storage and scanning technology, 68.
M. Spajer, Optics Comm. T.L. Ferrell, Phys. Rev. B M. Spajer, SPIE, Optical Proc. Vol. 1139 ( 1989) p.
D. Courjon et al. / Optics Communications I10 (1994) 7- I2 M. Chudgar, A. Choo, H. Jackson, G. de Brabander, M. Kumar and J. Boyd, Photon scanning tunneling of optical channel waveguides, Second International Conference on Near Field Optics NF02, Raleigh, USA ( 1993). P. Dawson, F. de Fornel and J.P. Goudonnet, Imaging of surface plasmon launch and propagation using a photon scanning tunneling microscope, Second International Conference on Near Field Optics, NF02, Raleigh, USA (1993). [6] 0. Bryngdahl, Appl. Optics 59 (1969) 1645. [7] H. Nassenstein, Phys. Lett. 28 A ( 1968) 249. [ 8] A. Meixner, M. Bopp and G. Tarrach, Direct measurement of standing evanescent waves with a photon scanning tunneling microscope, Appl. Optics, to be published.
[ 91 J. Mertz, M. Hipp, J. Mlynek and 0. Marti, Optical nearfield imaging with a semiconductor probe tip, Appl. Phys. Lett., to be published. [ IO] A. Manallah, Etude du dtcalage longitudinal et du dtcalage transversal d’un faisceau lumineux en reflexion totale: mesure par detection heterodyne, These Sciences pour TIngCnieur, University of Franche-Comte, Besancon, 1988. [ll ] M. Born and E. Wolf, Principles of Optics (Pergamon Press, 1959) p. 332. ]l2 ] D.W. Pohl, D. Courjon, C. Bainier, A. Dereux and H. Heinzelmann, Optical tunneling through adjustable liquid metal gap, Proceedings NATO Vol. 242 ( 1992) p. 46.