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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 15 — Jul. 23, 2007
  • pp: 9129–9138
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Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays

Michael Mrejen, Abraham Israel, Hesham Taha, Mila Palchan, and Aaron Lewis  »View Author Affiliations


Optics Express, Vol. 15, Issue 15, pp. 9129-9138 (2007)
http://dx.doi.org/10.1364/OE.15.009129


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Abstract

Extra ordinary transmission through arrays of subwavelength apertures has been investigated using near-field scanning optical microscopy. For such studies arrays were fabricated to give maximum resonance enhancement of light transmission at the wavelength of illumination that was used (532 nm). To define this enhancement a design was employed that allowed in one field of view of a near-field image the investigation of single apertures of dimension that was similar to what was incorporated into the sub-wavelength hole array. Significant asymmetry in the transmission and the propagation of the light along the aperture array was detected. This non-uniformity could be explained by polarization of the incident light, edge effects and the geometry of the array. The results support a hypothesis of both enhanced transmission due to surface plasmons and a non-diffracting beaming as a function of distance effect in the propagation of the light from the array.

© 2007 Optical Society of America

1. Introduction

More than two decades ago Lewis and co-workers investigated plane wave light transmission and the transmission of fluorescence through nano aperture arrays in gold and aluminum films [1

1. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500Å resolution microscope,” Ultramicroscopy 13, 227–231 (1984). [CrossRef]

-2

2. E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, “Near-Field Scanning Optical Microscopy (NSOM) Development and Biophysical Applications,” Biophys. J. 49, 269–279 (1986). [CrossRef] [PubMed]

]. They reported that the transmission of light from such subwavelength aperture arrays was larger than the weak transmission that would have been predicted theoretically by the Bethe-Bouwkamp model where the transmission T(dλ)4. In this equation “d” is the diameter of the aperture and λ is the wavelength of the light [3

3. H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (+). [CrossRef]

, 4

4. C. J. Bouwkamp, “On Bethe’s Theory of Diffraction by Small Holes,” Philips Res. Rep. 5, 321–332 (1950).

]. More recently, the large transmission property of such nano-hole arrays has been explained as an effect involving surface plasmons (SPs) [5

5. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

,6

6. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998). [CrossRef]

].

Since Ebbesen’s paper in 1998, nano-holes arrays have generated both theoretical and experimental interest in order to understand the physics involved in the Extraordinary Optical Transmission (EOT) through such arrays [6

6. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998). [CrossRef]

-10

10. C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

]. The experimental investigations undertaken have generally focused on far-field optics. Nonetheless, the optical near-field plays a major role in the enhancement process and so is integral to developing a full understanding. As a result a theoretical study of the optical characteristics in the near-field of such holes in a silver film has been published by Salomon et al [11

11. L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

].

The structure investigated was constructed using focused ion beam milling in gold films deposited on glass. NSOM imaging was done in collection mode while the single apertures and hole arrays were illuminated in the far field using plane wave illumination. In this configuration, surface plasmons are excited through the periodicity of the structure. The cantilevered optical fiber probe used in these NSOM measurements allowed for simultaneous topographic imaging and permitted accurate correspondence of the light distribution with the topography. The NSOM System used enabled independent tip and sample scanning. Thus the sample could be nanometrically aligned with respect to the input illuminating light source and could be held rigidly constant to the input light source while the probe scanner was activated to image the distribution of the light coming through the single apertures and the aperture arrays without the need to scan the sample.

2. Design and fabrication of the sub-wavelength nano-holes.

The resonant condition for the surface plasmon generation is given by Raether [16

16. H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).

]

ksp=k0sinθ±iGx±jGy
(1)

Where k⃗ sp is the SP dispersion, k⃗ 0 is the wave vector of the incident light, G⃗ x and G⃗y are the reciprocal lattice vectors associated with the two periodicities of the array and i and j are integers. For a square array, |G⃗x|=|G⃗y|=2π/a 0, where a 0 is the period. The SP dispersion relation is given by

ksp=2πλ(εmεdεm+εd)12
(2)

εd,εm are the dielectric constants for the dielectric and the metal (its real part) respectively. Note that for metals and for gold particularly εm is a function of the wavelength. Combining (1),(2) and assuming normal incidence, we obtain

a0=λ((i2+j2)εm+εdεmεd)12
(3)

Eq. (3) gives in fact the period needed to couple incoming light of wavelength λ with SP at the interface (εd|εm).

In view of the above in order to investigate in the same field of view an isolated hole relative to the aperture array we had to place the single aperture in a way that the SPs generated by the array did not affect its characteristics. An expression for the distance of the SP decay to 1/e of its intensity is given in [16

16. H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).

]

Li=(2Im[ksp])1
(4)

with

Im[ksp]=2πλ(Re[εm]εdRe[εm]+εd)32Im[εm]2Re[εm]2
(5)

From this analysis and using data for gold from [17

17. P. B. Johnson and R. Christie, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

], we set the different lengths needed for the fabrication of the samples. First, the period is chosen to be a 0~280 nm i.e. the one for the set (0,1) which is the one which gives the maximum enhancement according to Salomon et al [11

11. L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

]. For 532 nm illumination this analysis indicated that the isolated holes had to be placed at a distance more than 545 nm from the array in order not to interact with the SP generated by the structure.

With these calculated parameters we fabricated the samples for optical characterization. The first step was to coat a standard microscope coverslip with a gold layer. This was achieved by thermal evaporation. Then the gold-coated coverslip was inserted into a Focused ion Beam (FIB). The FIB (FEI Strata 400 STEM DualBeam) was used to mill the nanoarrays and nanoholes in a particular pattern that enable a simultaneous study and comparison of the behavior of nanoholes in an array and of single nanoholes [Fig. 1(a)]. The diameter of the nanoholes milled was 135 nm, the periodicity of the array 330 nm [Figs. 1(b) and 1(c)]. The measured thickness of the gold film was ~250 nm [Fig. 1(d)].

In addition, we have perforated near every nanohole array-a single aperture with a considerably larger dimension (diameter~400 nm) to readily find in the on-line optical microscope the area of interest. This hole was positioned in a way so that it did not interfere with the SPs excitation and propagation process.

Fig. 1. SEM images of a typical sample fabricated by FIB. (a),(b),(c) views of the sample with typical dimension achieved. (d) lateral cut showing depth of the holes and thickness of the gold coating.

Particular attention was given to minimizing the depth of the milling into the glass by minimizing the exposure time of the beam while keeping the ion beam stable. Fig. 1(d) shows the minimal depth achieved (160nm) which is still too short compared to the wavelength used (532nm) to have wave guiding effects.

3. Experimental methods for optical characterization.

For the NSOM measurements a MultiView 2000 Scanned Probe Microscope/NSOM System was used (Nanonics Imaging Ltd., Jerusalem, Israel). The SPM head was mounted into a dual 4pi microscope and the system enabled Atomic Force Microscopy (AFM) imaging with online NSOM while the optical axis from above and below remained completely free. The sample was illuminated with a 532 nm Nd:YAG laser from below through the inverted microscope with a X10, NA 0.25 objective (Fig. 2). The sample scanner was used to position the nano-holes relative to the incoming light. With the sample accurately held in position, a 200 nm aperture NSOM probe was scanned above the nano-apertures to collect the light and transmit it through the optical fiber onto an avalanche photo diode. An AFM image is obtained online. The independent probe and sample piezo scanners were of great importance for characterizing the propagation of light through such apertures and this will be discussed below.

Fig. 2. Schematic of the experimental setup for the near field and far field characterization of the nano-holes.

4. Results and discussion

In this section we present results obtained for two types of experiments. The first set of results is obtained while the probe is in contact with the surface. This experiment allowed for determining the enhancement of the hole array relative to a single aperture and highlighted the importance of the periodicity on the observed enhancement. Furthermore the results also indicated the importance of the input polarization. Finally, in a second set of experiments the light intensity propagation in a direction perpendicular to the plane of the array was monitored to address the suggestion that such arrays allow for propagation with reduced diffraction [21

21. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820. [PubMed]

, 22

22. M. W. Docter, I. T. Young, O. M. Piciu, A. Bossche, P. F. A. Alkemade, P. M. Van Den Berg, and Y. Garini, “Measuring the wavelength-dependent divergence of transmission through sub-wavelength hole-arrays by spectral imaging,” Opt. Express 14, 9477 (2006). [CrossRef] [PubMed]

].

4.1 Near-field distribution at the surface

4.1.1 Enhancement and periodicity-linked features

In order to show the relative enhancement, a field of view that included both an array of apertures and single holes was scanned. Since these measurements were made with the probe in contact it was possible to obtain an online AFM topographic image. This enabled the correlation between the NSOM data and the topography of the area scanned. The results are shown below in Fig. 3. In the AFM picture the holes are clearly distinguishable (see arrows in Fig. 3(a): red for the single 135 nm single holes and blue for the 400 nm hole). However, on the NSOM picture only the array and the 400 nm hole are seen. In the NSOM image, the 400 nm hole gives a bright spot which is expected due to its large diameter. The single holes are not seen in this NSOM image because of the very low relative transmission through them and the scaling of the entire image which is adjusted for the brightest regions in the image. The data showed that the single 135 nm apertures had a transmission that was 40 times less than what was seen for a similar aperture in the array.

Fig. 3. (a). Online AFM and (b) NSOM images

If the entire image is rescaled then the 135 nm single apertures become clearly visible as seen in Fig. 4. However, under these conditions the aperture array and the 400 nm aperture array are in saturation as seen in Fig. 4.

Fig. 4. NSOM image in Fig. 3 after re-scaling.

It is important to stress that the enhancement noted above is obtained by comparing intensities acquired at the same time from the array and single nano holes illuminated under the same conditions. As seen in the data there are two single holes with 135 nm diameter and the comparison of the intensity through the holes in the array to either one of these holes indicated the same enhancement.

4.1.2 Polarization and symmetry effects

In Fig. 5 results are obtained for an undamaged array in the near-field.

Fig. 5. (a). AFM image of the array; (b) NSOM image of the same region.

There are two striking facts arising from the NSOM image of the array. The first is the non-uniformity of the light distribution over the array. This non-uniformity is a product of several facts as described by Bravo-Abad et al [19

19. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garcia-Vidal, L. Martin-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nature Phys. 2, 120 (2006). [CrossRef]

]. In spite of the symmetrical geometry of the array, the light distribution is not symmetric. The break in this symmetry is induced by the polarization of the light. The polarized light creates a “preferred” direction and makes the structure behave in different ways in x and in y and in addition there is sensitivity to the angle of incidence of the exciting light. This is noted by Bravo-Abad et al [19

19. J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garcia-Vidal, L. Martin-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nature Phys. 2, 120 (2006). [CrossRef]

] and from the similarity of our results to their analysis we can suggest a 5° tilt of the sample to the incident radiation. Additionally, the non-uniformity is caused by the finite size of the array or in other words edge effects. The edge effects break the periodicity. At these edges the SPs can be reflected giving rise to interference phenomena inside the array between propagating SPs and reflected ones.

A second striking fact, which can be deduced from Fig. 5(b), is linked to the SPs preferred propagation direction induced by the periodicity of the array and its design. Consider two line profiles: one taken in the X direction and one taken in the Y direction (Fig. 6). It is clearly seen that in the y direction the spots arising from the holes are less distinguishable than the spots in the X direction. To quantify this difference, we chose to use here the concept of contrast defined by Michelson [20

20. A. A. Michelson, Studies in Optics (University of Chicago Press, 1927).

]:

C=ImaxIminImax+Imin
(6)

The contrast is bounded between 0 and 1 with C→1 indicating high contrast or as seen in the NSOM image of Fig. 5 the light spots being well defined and distinguishable.

Fig. 6. (a). line profile over the array taken in the x direction (b) line profile over the array taken in the y direction. (The white line indicates where the profile was taken)

Based on these line profiles, the C parameter is calculated to be 0.52 in X and 0.07 in Y. Thus, the holes in the x direction exhibit much higher contrast than in the y direction.

A possible explanation could be that the NSOM collecting aperture has a finite dimension which could gives rise to a convolution effect. A simulation of such an effect is seen in Fig. 7.

Fig. 7. Simulation of the convolution effect when imaging a 9x9 hole array with a 200 nm NSOM aperture. (left) object, (middle) imaging probe, (right) resulting image (scale is in pixels, 1 pixel=30 nm).

The problem with this explanation is that it does not account for the difference observed between the x and the y direction since such a convolution would uniformly blur the image. This difference is an expression of the Surface-Plasmon based effects that take place in the sample. Salomon et al [11

11. L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

] have suggested that the surface Plasmon mode that gives the largest enhancement is the (0, 1) mode and according to Eq. 3 this would occur for a period of 280 nm for a wavelength of 532 nm. However Eq. 3 does not take into account the finite dimension of the apertures in the array and such a finite dimension would increase the dimension of the period where the resonance would occur. Accordingly, the sample was chosen to support the (0, 1) SP mode of propagation by using a slightly larger period (330 nm) than suggested by the simplified model. This mode means that the SPs generated propagate in the y direction. The difference of contrast seen between the x direction and the y direction is in fact the expression of the SPs preferred propagation direction in y.

With this analysis of the behavior of the array in the near-field which support the view of surface plasmon involvement in the phenomena observed, we turn our attention to the investigation of the propagation properties of the light in a direction perpendicular to the plane of the array.

4.1.3 Propagation of the light as a function of distance from the nano holes array

The propagation of light as a function of distance from the array is investigated by sectioning the light field at different heights within a distance of one wavelength from the surface. To do so the NSOM probe is brought into contact with the surface and retracted gradually with the help of the upper piezo probe scanner (Fig. 8) while the sample is kept rigidly constant with voltage maintained on the piezos of the lower sample scanner. At each step in z (100 nm) an x,y image was obtained to investigate the (x,y) light distribution at each specific z (height) distance. We chose to study the light propagation within one wavelength i.e. ~600 nm and collected a total of six slices. The height steps were chosen to highlight any non-diffracting aspect of the aperture array.

Fig. 8. schematic of the experiment conducted.

With the light kept with a polarization in the x-direction, we present a set of images obtained in Fig. 9.

Fig. 9. (a). to (f) xy optical sections at different z distances from the sample. The color map depicted in (a) is common to all the six images. Arrows in (e) and (f) point to the light coming from the 400 nm aperture which becomes visible at larger z distances due to diffraction.

The light spot indicated by the yellow arrow in Figs. 9(a) and 9(b) is arising from a single 135 nm diameter hole while the one pointed in Figs. 9(e) and 9(f) arises from the 400 nm hole. The first interesting feature seen from these results is that while the single isolated aperture is detected only in the two first images 9(a) and 9(b), the array is seen with high signal to noise on all the six images and essentially keeps the same overall dimensions at least for 200 nm more than the single aperture.

It could be thought that as the tip moves away from the array it collects diffracted light from more and more holes. When the tip is contact, it collects light exclusively from the hole it is above but when it retracts from the surface, surrounding holes contribute to the intensity. According to this explanation, one expects that the overall dimensions of the “array”, or more precisely the pattern formed by the light diffracted from the nano holes constituting the array, should grow with a peak intensity that continuously decreases. This is obviously not the case here. The light arising from the isolated nano hole [9(a) and 9(b)] is barely visible at 200 nm, which can be predicted from the sub-wavelength nature of the hole giving rise mostly to evanescent waves that disappear within one wavelength. However, diffracted light from the array, composed exactly of nano holes with the same dimension as the isolated aperture, are observed over the entire Z range that was investigated and return the overall dimension of the array as in the near-field for much of this z range.

The data shows that for the single hole, the angle of diffraction is as big as 69 degrees while the peak intensity is decreased by a factor of 4 after only 100 nm of propagation. However, for the array the diffraction angle is 19 degrees and the peak intensity is decreased only by a factor of 4/5 for a propagation of 500 nm. This clearly indicates that the light emerging from the holes in the array propagates in a completely different manner than it propagates from a single hole of the same characteristics.

One suggestion for this effect could be what has been termed a beaming effect. It has been shown [21

21. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820. [PubMed]

, 22

22. M. W. Docter, I. T. Young, O. M. Piciu, A. Bossche, P. F. A. Alkemade, P. M. Van Den Berg, and Y. Garini, “Measuring the wavelength-dependent divergence of transmission through sub-wavelength hole-arrays by spectral imaging,” Opt. Express 14, 9477 (2006). [CrossRef] [PubMed]

] that plasmonic devices of the kind that we are treating here i.e. apertures with periodic structures surrounding them transmit light in a way that does not obey classical diffraction theory. A propagating light beam transmitted through a subwavelength aperture should become evanescent and the intensity as a function of distance from the aperture should disappear nearly exponentially. The fact that propagating light transmitted by sub-wavelength apertures in the array can be observed with little diffraction at the edges of the array indicates a high degree of directionality that is not classically seen and can be ascribed to the involvement of surface plasmons. This directionality directly arises from the SP-light coupling condition of Eq. (1) i.e. that by choosing the proper periodicity, one can tailor the propagation direction of the light coupled to the SPs on the output surface. In our case, the periodicity was chosen to enable SP-light coupling on the input side for a normal incident wave, it is then expected that on the output side the light propagates normal to the surface. The diffraction observed can be accounted for the finite size of the array, but yet this diffraction is much less than the one observed from the isolated hole.

5. Conclusion

This work highlights once again the importance of near-field optics for investigation nanophotonic devices and for further characterizing the basis of EOT. The data we have obtained support both the suggestion of a significant enhancement in the transmission of light through such apertures in an appropriately constructed array and also give credibility for significant directionality in the propagation of light as a function of distance away from such an array structure.

Acknowledgments

The authors wish to thank The Horowitz Foundation, The Israel Ministry of Science, The US Israel Binational Foundation and The Human Frontier Program for supporting this research. The technical staff of Nanonics Imaging Ltd. is acknowledged. Use of the Focused Ion Beam at the Russell Berrie Nanotechnology Institute at the Israel Institute of Technology (Technion) is also acknowledged.

References and links

1.

A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, “Development of a 500Å resolution microscope,” Ultramicroscopy 13, 227–231 (1984). [CrossRef]

2.

E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, “Near-Field Scanning Optical Microscopy (NSOM) Development and Biophysical Applications,” Biophys. J. 49, 269–279 (1986). [CrossRef] [PubMed]

3.

H. A. Bethe, “Theory of Diffraction by Small Holes,” Phys. Rev. 66, 163–182 (+). [CrossRef]

4.

C. J. Bouwkamp, “On Bethe’s Theory of Diffraction by Small Holes,” Philips Res. Rep. 5, 321–332 (1950).

5.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

6.

H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, “Surface plasmons enhance optical transmission through subwavelength holes,” Phys. Rev. B 58, 6779–6782 (1998). [CrossRef]

7.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of extraordinary optical transmission through subwavelength hole arrays,” Phys. Rev. Lett. 86, 1114–1117 (2001). [CrossRef] [PubMed]

8.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Deveaux, and T. W. Ebbesen, “Surface Plasmon Polaritons and their role in the enhanced transmission of light through periodic arrays of subwalength holes in a metal film,” Phys. Rev. Lett. 92, 107401(2004). [CrossRef] [PubMed]

9.

L. Martin-Moreno and F. J. Garcia-Vidal, “Optical tranmission through circular hole arrays in optically thick metal films,” Opt. Express 12, 3619 (2004). [CrossRef]

10.

C. Genet and T. W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

11.

L. Salomon, F. Grillot, A. V. Zayats, and F. de Fornel, “Near-field distribution of optical transmission of periodic subwavelength holes in a metal film,” Phys. Rev. Lett. 86, 1110–1113 (2001). [CrossRef] [PubMed]

12.

C. Sonnichsen, A. C. Duch, G. Steininger, M. Koch, G von Plessen, and J. Feldmann, “Launching surface plasmons into nanoholes in metal films,” Appl. Phys. Lett. 76, 140–142 (2000). [CrossRef]

13.

E. X. Jin and X. Xu, “Enhanced optical near field from a bowtie aperture,” Appl. Phys. Lett. 88, 153110 (2006). [CrossRef]

14.

Y. Poujet, M. Roussey, J. Salvi, F. I. Baida, D. Van Labeke, A. Perentes, C. Santschi, and P. Hoffmann, “Super-transmission of light through subwavelength annular aperture arrays in metallic films: spectral analysis and near-field optical images in the visible range,” Photonics and Nanostructures- Fundamentals and Applications 4, 47–53 (2006). [CrossRef]

15.

D. Egorov, B. S. Dennis, G. Blumberg , and M. I. Haftel, “Two-dimensional control of surface plasmons and directional beaming from arrays of subwavelength apertures,” Phys. Rev. B 70, 033404 (2004). [CrossRef]

16.

H. Raether, Surface Plasmons on smooth and rough surfaces and on gratings (Springer-Verlag, Berlin, 1988).

17.

P. B. Johnson and R. Christie, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

18.

H. J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629 (2004). [CrossRef] [PubMed]

19.

J. Bravo-Abad, A. Degiron, F. Przybilla, C. Genet, F. J. Garcia-Vidal, L. Martin-Moreno, and T. W. Ebbesen, “How light emerges from an illuminated array of subwavelength holes,” Nature Phys. 2, 120 (2006). [CrossRef]

20.

A. A. Michelson, Studies in Optics (University of Chicago Press, 1927).

21.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820. [PubMed]

22.

M. W. Docter, I. T. Young, O. M. Piciu, A. Bossche, P. F. A. Alkemade, P. M. Van Den Berg, and Y. Garini, “Measuring the wavelength-dependent divergence of transmission through sub-wavelength hole-arrays by spectral imaging,” Opt. Express 14, 9477 (2006). [CrossRef] [PubMed]

OCIS Codes
(050.1220) Diffraction and gratings : Apertures
(050.1940) Diffraction and gratings : Diffraction
(160.4760) Materials : Optical properties
(180.5810) Microscopy : Scanning microscopy
(240.6680) Optics at surfaces : Surface plasmons
(260.3910) Physical optics : Metal optics

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 22, 2007
Revised Manuscript: July 4, 2007
Manuscript Accepted: July 5, 2007
Published: July 10, 2007

Citation
Michael Mrejen, Abraham Israel, Hesham Taha, Mila Palchan, and Aaron Lewis, "Near-field characterization of extraordinary optical transmission in sub-wavelength aperture arrays," Opt. Express 15, 9129-9138 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9129


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References

  1. A. Lewis, M. Isaacson, A. Harootunian, and A. Muray, "Development of a 500Å resolution microscope," Ultramicroscopy 13, 227-231 (1984). [CrossRef]
  2. E. Betzig, A. Lewis, A. Harootunian, M. Isaacson, and E. Kratschmer, "Near-Field Scanning Optical Microscopy (NSOM) Development and Biophysical Applications," Biophys. J. 49, 269-279 (1986). [CrossRef] [PubMed]
  3. H. A. Bethe, "Theory of Diffraction by Small Holes," Phys. Rev. 66, 163-182 (1944). [CrossRef]
  4. C. J. Bouwkamp, "On Bethe’s Theory of Diffraction by Small Holes," Philips Res. Rep. 5, 321-332 (1950).
  5. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
  6. H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998). [CrossRef]
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