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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 15 — Jul. 19, 2010
  • pp: 15725–15731
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Phase-sensitive imaging of diffracted light by single nanoslits: measurements from near to far field

Hyun-woo Kihm, Q. H. Kim, D. S. Kim, K. J. Ahn, and J. H. Kang  »View Author Affiliations


Optics Express, Vol. 18, Issue 15, pp. 15725-15731 (2010)
http://dx.doi.org/10.1364/OE.18.015725


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Abstract

We perform phase-sensitive imaging of optical wavefront emanating from a single nanoslit and propagating into free space by using scattering type near-field scanning optical microscope combined with an optical interferometer. By analyzing polarization resolved optical amplitudes and phases, the propagation directions of surface waves are determined and the phase difference between two orthogonal polarization components of the surface wave are discussed for increasing distance from the slit.

© 2010 Optical Society of America

1. Introduction

Spatially oscillating electromagnetic (EM) fields are completely defined only when both amplitude and phase are simultaneously known. The knowledge on spatial distribution of optical field is especially important in optical phenomena of subwavelength structures where the behavior of the optical polarization and the phase is not simply estimated. Complex diffraction phenomena caused by interaction between nanostructures are being exploited to efficiently manipulate EM fields, for instances, focussing or guiding of light using nanoslits [1

1. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009). [CrossRef]

], grooves [2

2. C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94, 111105 (2009). [CrossRef]

], and holes [3

3. D. van Oosten, M. Spasenovic, and L. Kuipers, “Nanohole Chains for Directional and Localized Surface Plasmon Excitation,” Nano Lett. 10, 286–290 (2010). [CrossRef]

, 4

4. L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, “Fourier plasmonics: Diffractive focusing of inplane surface plasmon polariton waves,” Appl. Phys. Lett. 91, 081101 (2007). [CrossRef]

]. For the design of optical antenna, spatial mapping of amplitude and phase performed in near-field regime is also crucial [5

5. M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3, 287–291 (2009). [CrossRef]

].

Measurement of optical amplitudes and phases on a few tens of nanometer resolution can be achieved by means of near-field scanning optical microscope (NSOM) combined with an interferometer [6–8

6. D.-S. Kim, J. Heo, S.-H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-Space Mapping of the Strongly Coupled Plasmons of Nanoparticle Dimers,” Nano. Lett. 9, 3619–3625 (2009). [CrossRef] [PubMed]

]. Among different types of phase-sensitive NSOM, heterodyne detection scheme is frequently used due to relatively low background noise. In this scheme the scattered light from the near-field probe is measured through lock-in detection at the beating frequency given by the probe and reference beam modulations [9

9. A. Nesci, R. Dandliker, and H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001). [CrossRef]

, 10

10. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006). [CrossRef]

]. However, heterodyne technique is not useful for measuring optical fields far away from surfaces, especially, where near-to-far field conversion occurs, because the optical signal modulated by the probe is mainly sensitive to the surface-probe optical interaction.

In this letter, we demonstrate phase-sensitive imaging of diffracted light by a single nanoslit using homodyne detection technique to perform height dependent measurement of optical amplitude and phase. We choose a single nanoslit as a test bed for our homodyne phase-sensitive NSOM measurement, because it is one of fundamental structures launching surface plasmon polariton (SPP) [11–17

11. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and Ch. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]

]. Cylindrical wavefronts emanating from the slit and propagating into free space up to a few wavelengths away from the slit are successfully reconstructed. Our phase-sensitive measurement performed on single slits provides information about propagation directions of surface waves and phase difference evolution between the horizontal and the vertical polarization components for increasing distance from the slit.

2. Experiments and Discussion

Figure 1 is a schematic of our homodyne phase-sensitive NSOM. Incident pulse laser (Mira900, Coherent) with spectral bandwidth less than 5 nm at 780 nm center wavelength is split into an excitation and a reference beam by the non-polarizing beam splitter (BS). The excitation beam illuminates a slit sample at the normal incidence from the bottom with the vertical polarization to the slit axis. A single slit with 300 nm width is perforated in a 150 nm thick gold film. The diffracted light from the slit is scattered at the apex of a commercial metal coated NSOM probe (Nanonics) with aperture diameter of 100 nm. A sufficiently blunt metal coated probe is used to suppress the image dipole effects [18

18. H. W. Kihm, K. G. Lee, D. S. Kim, and K. J. Ahn, “Dual mode near-field scanning optical microscopy for near-field imaging of surface plasmon polariton,” Opt. Commun. 282, 2442–2445 (2009). [CrossRef]

] which strongly modify the scattering signal on metal surfaces [19

19. K. G. Lee, K. J. Ahn, H. W. Kihm, J. S. Ahn, T. K. Kim, S. Hong, Z. H. Kim, and D. S. Kim, “Surface plasmon polariton detection discriminating the polarization reversal image dipole effects,” Opt. Express 16, 10641–10649 (2008). [CrossRef] [PubMed]

]. The scattered light from the probe apex is guided toward the second non-polarizing BS to be mixed with the reference beam, which is retro reflected by the moving mirror (Fig. 1).

The moving mirror driven by a saw-tooth waveform with modulation frequency of Ω (500 Hz) provides an additional optical phase to the reference beam. We note that the saw-tooth waveform gives an ideal sinusoidal interference signal between the scattered light and the reference beam, while sinusoidal or triangular waveforms result in distorted interference signals. This is because sinusoidal or triangle waveform needs both of its amplitude and phase to be controlled simultaneously to give a sinusoidal interference signal, which is ideal for lock-in detection operated in a single frequency. However, controlling the phase of the waveform is difficult because the phase of the target signal ϕsig [Eq. (1)] is not constant but dependent on the probe position. On the other hands, saw-tooth waveform only needs its amplitude controlled to calibrate the modulation amplitude of the moving mirror to be equal to the half wavelength of the incident light, which gives sinusoidal interference signal.

Co-linearly recombined reference beam with the scattered light generates an interference signal which is described by

I=Esig2+Eref2+2EsigErefcos(ϕsigϕref(t)),
(1)

where E sig(ref) and ϕ sig(ref) are electric field amplitudes and phases of signal (reference) beam, respectively. Time varying optical phase of the reference beam makes the simultaneous detection of Esig and ϕsig feasible through the lock-in detection at the modulation frequency of ϕref (Ω). The interference signal is split again by the polarizing BS for polarization resolved detections.

Fig. 1. The experimental setup: scattering type NSOM is combined with an optical interferometer, which is comprised of 1,5:non-polarizing BS, 2: linear polarizer, 3: half wave plate, 4: NSOM probe, 6: polarizing BS, 7: moving mirror modulated by saw-tooth waveform. Arrowed lines among the optical components represents beam path of signal excitation beam (solid) and reference beam (dashed), respectively.
Fig. 2. Visualized optical wavefronts of light diffracted by the single slit. (a, d) Spatial mappings of the measured amplitudes multiplied by sine functions of phases. (b, e) Spatial phase mappings. (c, f) Linear profiles along the arrowed white lines in (b) and (e), respectively for the horizontal (left panel) and the vertical (right panel) polarization component. Dashed lines are guiding for eyes.

Height dependent phase-sensitive measurements of the diffracted light from the slit are performed through sample scanning geometry at a constant probe height ranging from 0.1 µm up to 2.8 µm. We visualize diffracted optical wavefronts in Fig. 2(a) and 2(d) by mapping the measured optical amplitudes multiplied by sine function of measured ϕsig.

While the wavefronts of the horizontal polarization component propagate into far-field with quasi cylindrical symmetry, those of the vertical polarization components propagate mostly in both side directions along the surface, as expected from theory [14

14. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005). [CrossRef]

, 20

20. H. W. Kihm, J. H. Kang, J. S. Kyoung, K. G. Lee, M. A. Seo, and K. J. Ahn, “Separation of surface plasmon polariton from nonconfined cylindrical wave launched from single slits,” Appl. Phys. Lett. 94, 141102 (2009). [CrossRef]

]. Figure 2(b) and 2(e) where measured phases are mapped as a function of position more clearly explain different wavefront propagation characteristics of two polarization components: while only radial equiphase lines are shown in the horizonal component (Fig. 2), a π-phase difference between the left and the right side of the slit and a phase-disjunction above the slit aperture can be seen in the vertical component (Fig. 2).

Cross sections in phase maps along the arrowed lines show two linear curves with opposite slopes as shown in Fig. 2(c) and 2(f). The absolute value of the slopes are obtained as (2.53± 0.03)π [µm −1], which shows good agreement with the wavenumber of the incident light (k 0 = 2.56π[µm −1]). The presented results indicate that our phase-sensitive NSOM can successfully measure propagating wavefronts in the near-field as well as far away from the surface.

Next, we investigate evolution of the phase relation between two polarization components in a close proximity of the metal surface. The phase relation is especially important for discriminating the non-confined cylindrical wave from SPP [20

20. H. W. Kihm, J. H. Kang, J. S. Kyoung, K. G. Lee, M. A. Seo, and K. J. Ahn, “Separation of surface plasmon polariton from nonconfined cylindrical wave launched from single slits,” Appl. Phys. Lett. 94, 141102 (2009). [CrossRef]

]. As presented in Fig. 3, hardly distinguishable mixture of SPP and the surface diffracted wave at distance of 1 µm from the slit [Fig. 3(a) and 3(b)] are clearly separated at 30 µm away from the slit [Fig. 3(e) and 3(f)]. By comparing field profiles of measured optical wavefronts along the horizontal line at a fixed height (0.1 µm), we can read phase differences of π and π/2 between the horizontal and the vertical polarization components at 1 µm [Fig. 3 (c)] and at 30 µm [Fig. 3(g)] from the slit, respectively.

The varying phase relation between two components for the increasing distances from the slit can be explained by a surface wave model composed of SPP and a cylindrical wave. In magnetic field representation two waves on the right side of the slit are written by

Hrad=H0(x)ei(kxx+kzz),Hspp=H1(x)ei(Re[kspp]x)κz,
(2)

where k0=kx2+kz2 and kspp are the wavenumbers of the cylindrical wave and SPP, κ=kspp2k02 the decay rate of SPP along the vertical axis. H 0 is the magnetic field strength of the cylindrical wave with 1/√x slit distance dependency [21–23

21. Y. Gravel and Y. Sheng, “Rigorous solution for the transient surface plasmon polariton launched by subwavelength slit scattering,” Opt. Express 16, 21903 (2008). [CrossRef] [PubMed]

], and H 1 is that of SPP with eIm(kspp) decay behavior [18

18. H. W. Kihm, K. G. Lee, D. S. Kim, and K. J. Ahn, “Dual mode near-field scanning optical microscopy for near-field imaging of surface plasmon polariton,” Opt. Commun. 282, 2442–2445 (2009). [CrossRef]

]. Note that the time-dependent term eiωt is suppressed throughout. The electric fields of SPP and the cylindrical wave are derived from Eq. (2) through Maxwell’s equations. Then, the horizontal and the vertical polarization component Ex and Ez of the electric field are obtained as

Ex=kzH0(x)ωε0ei(kxx+kzz)+κH1(x)ωε0ei(Re[kspp]x+π2)κz,
(3)
Ez=kxH0(x)ωε0ei(kxx+kzz+π)+ksppH1(x)ωε0ei(Re[kspp]x+π)κz.
(4)

When the cylindrical wave is predominant over SPP near the slit, the surface wave can be approximated by the first terms of the right hand side of Eq. (3) and (4): there exists a π phase difference between two polarization components. As the distance from the slit increases to about 30 µm, SPP begins to predominate the cylindrical wave due to the fact that SPP has a negligible decay constant along the metal surface whereas the non-confined cylindrical wave decays with dependence on the reciprocal distance [20

20. H. W. Kihm, J. H. Kang, J. S. Kyoung, K. G. Lee, M. A. Seo, and K. J. Ahn, “Separation of surface plasmon polariton from nonconfined cylindrical wave launched from single slits,” Appl. Phys. Lett. 94, 141102 (2009). [CrossRef]

]. Therefore, the surface wave in this regime is decided by the second term in each equation, and a π/2 phase difference between two components is expected as our experimental result presents. When the phase difference would be measured on the left side of the slit, zero phase difference is observed in the proximity of the slit, because in this case kx in Eq. (4) should have a negative value due to the reversed propagation direction of SPP.

Fig. 3. Optical surface wavefronts measured at 1 µm (left panel) and 30 µm (right panel) away from the right side of the slit. (a, e) The horizontal (x-pol) polarization components. (b, f) The vertical (z-pol) polarization components. (c, g) Cross sections of the wavefronts along the scan line at a constant height (0.1 µm) from the surface. (d, h) FDTD simulation results.

We note that the observation of the phase difference near the slit is possible only when the height of NSOM probe position is large enough to detect the vertical wavevector component kz [Eq. (3)]. FDTD simulation results at 0.3 µm height [Fig. 3(d) and 3(h)] show good agreement with our experimental results [Fig. 3(c) and 3(g)] at 0.1 µm, while only π/2 phase difference is observed with less than 0.1 µm height. The discrepancy of scanning height between FDTD and experimental results can be attributed to the scattering signal from the probe shaft which mainly detects the cylindrical wave in the free space.

Fig. 4. Phase difference between horizontally and vertically polarized surface waves as a function of distance from the slit. NSOM measurements (open circles) and FDTD calculations (red dashed lines) are compared.

3. Conclusion

In conclusion, we demonstrate phase-sensitive near-field imaging of diffracted light from a single nanoslit. Homodyne detection technique is used for height dependent phase-sensitive measurement to visualize the cylindrical wave and SPP emanating from the slit. Analysis of the measured phase map determines the propagation direction of the surface wavefronts. Furthermore, varying phase difference between the horizontal and the vertical polarization component of the electric field is observed for increasing distance from the slit. We believe that our phase-sensitive measurement technique will be beneficial for investigating complex diffraction phenomena caused by nano structures and interactions among them.

Acknowledgements

This work was supportedby the Korea Science and Engineering Foundation (KOSEF) (SRC, No:R11-2008-095-01000-0) and the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) (No:2009-0071309), KICOS (GRL, K20815000003) and the Seoul R&BD Program(10543).

References and links

1.

L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009). [CrossRef]

2.

C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94, 111105 (2009). [CrossRef]

3.

D. van Oosten, M. Spasenovic, and L. Kuipers, “Nanohole Chains for Directional and Localized Surface Plasmon Excitation,” Nano Lett. 10, 286–290 (2010). [CrossRef]

4.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, “Fourier plasmonics: Diffractive focusing of inplane surface plasmon polariton waves,” Appl. Phys. Lett. 91, 081101 (2007). [CrossRef]

5.

M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the near-field oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3, 287–291 (2009). [CrossRef]

6.

D.-S. Kim, J. Heo, S.-H. Ahn, S. W. Han, W. S. Yun, and Z. H. Kim, “Real-Space Mapping of the Strongly Coupled Plasmons of Nanoparticle Dimers,” Nano. Lett. 9, 3619–3625 (2009). [CrossRef] [PubMed]

7.

I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type Scanning Near-Field Optical Microscope,” Opt. Express 13, 5553–5564 (2005). [CrossRef] [PubMed]

8.

M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett. 102, 033902 (2009). [CrossRef] [PubMed]

9.

A. Nesci, R. Dandliker, and H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001). [CrossRef]

10.

N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free near-field spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006). [CrossRef]

11.

D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and Ch. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]

12.

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]

13.

F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005). [CrossRef]

14.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005). [CrossRef]

15.

Y. S. Jung, J. Wuenschell, T. Schmidt, and H. K. Kim, “Near-to far-field imaging of free-space and surface-bound waves emanating from a metal nanoslit,” Appl. Phys. Lett. 92, 023104 (2008). [CrossRef]

16.

H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q-Han Park, “Control of surface plasmon generation efficiency by slit-width tuning,” Appl.Phys. Lett. 92, 051115 (2008). [CrossRef]

17.

K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photonics 1, 53–56 (2007). [CrossRef]

18.

H. W. Kihm, K. G. Lee, D. S. Kim, and K. J. Ahn, “Dual mode near-field scanning optical microscopy for near-field imaging of surface plasmon polariton,” Opt. Commun. 282, 2442–2445 (2009). [CrossRef]

19.

K. G. Lee, K. J. Ahn, H. W. Kihm, J. S. Ahn, T. K. Kim, S. Hong, Z. H. Kim, and D. S. Kim, “Surface plasmon polariton detection discriminating the polarization reversal image dipole effects,” Opt. Express 16, 10641–10649 (2008). [CrossRef] [PubMed]

20.

H. W. Kihm, J. H. Kang, J. S. Kyoung, K. G. Lee, M. A. Seo, and K. J. Ahn, “Separation of surface plasmon polariton from nonconfined cylindrical wave launched from single slits,” Appl. Phys. Lett. 94, 141102 (2009). [CrossRef]

21.

Y. Gravel and Y. Sheng, “Rigorous solution for the transient surface plasmon polariton launched by subwavelength slit scattering,” Opt. Express 16, 21903 (2008). [CrossRef] [PubMed]

22.

S.-H. Chang, S. K. Gray, and G. C. Schatz, “Surface plasmon generation and light transmission by isolated nanoholes and arrays of nanoholes in thin metal films,” Opt. Express 13, 3150 (2005). [CrossRef] [PubMed]

23.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006). [CrossRef]

OCIS Codes
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(240.6690) Optics at surfaces : Surface waves
(110.3175) Imaging systems : Interferometric imaging

ToC Category:
Diffraction and Gratings

History
Original Manuscript: May 12, 2010
Revised Manuscript: July 1, 2010
Manuscript Accepted: July 1, 2010
Published: July 9, 2010

Citation
Hyun-woo Kihm, Q. H. Kihm, D. S. Kim, K. J. Ahn, and J. H. Kang, "Phase-sensitive imaging of diffracted light by single nanoslits: measurements from near to far field," Opt. Express 18, 15725-15731 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15725


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References

  1. L. Verslegers, P. B. Catrysse, Z. Yu, J. S. White, E. S. Barnard, M. L. Brongersma, and S. Fan, “Planar lenses based on nanoscale slit arrays in a metallic film,” Nano Lett. 9, 235–238 (2009). [CrossRef]
  2. C. Zhao, J. Wang, X. Wu, and J. Zhang, “Focusing surface plasmons to multiple focal spots with a launching diffraction grating,” Appl. Phys. Lett. 94, 111105 (2009). [CrossRef]
  3. D. van Oosten, M. Spasenovic, and L. Kuipers, “Nanohole Chains for Directional and Localized Surface Plasmon Excitation,” Nano Lett. 10, 286–290 (2010). [CrossRef]
  4. L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, “Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves,” Appl. Phys. Lett. 91, 081101 (2007). [CrossRef]
  5. M. Schnell, A. Garcia-Etxarri, A. J. Huber, K. Crozier, J. Aizpurua, and R. Hillenbrand, “Controlling the nearfield oscillations of loaded plasmonic nanoantennas,” Nat. Photonics 3, 287–291 (2009). [CrossRef]
  6. D.-S. Kim, J. Heo, S.-H. Ahn, S. W. Woo Han, W. S. Yun, and Z. H. Kim, “Real-Space Mapping of the Strongly Coupled Plasmons of Nanoparticle Dimers,” Nano Lett. 9, 3619–3625 (2009). [CrossRef] [PubMed]
  7. I. Stefanon, S. Blaize, A. Bruyant, S. Aubert, G. Lerondel, R. Bachelot, and P. Royer, “Heterodyne detection of guided waves using a scattering-type Scanning Near-Field Optical Microscope,” Opt. Express 13, 5553–5564 (2005). [CrossRef] [PubMed]
  8. M. Burresi, R. J. P. Engelen, A. Opheij, D. van Oosten, D. Mori, T. Baba, and L. Kuipers, “Observation of Polarization Singularities at the Nanoscale,” Phys. Rev. Lett. 102, 033902 (2009). [CrossRef] [PubMed]
  9. A. Nesci, R. Dandliker, and H. P. Herzig, “Quantitative amplitude and phase measurement by use of a heterodyne scanning near-field optical microscope,” Opt. Lett. 26, 208–210 (2001). [CrossRef]
  10. N. Ocelic, A. Huber, and R. Hillenbrand, “Pseudoheterodyne detection for background-free nearfield spectroscopy,” Appl. Phys. Lett. 89, 101124 (2006). [CrossRef]
  11. D. S. Kim, S. C. Hohng, V. Malyarchuk, Y. C. Yoon, Y. H. Ahn, K. J. Yee, J. W. Park, J. Kim, Q. H. Park, and Ch. Lienau, “Microscopic origin of surface-plasmon radiation in plasmonic band-gap nanostructures,” Phys. Rev. Lett. 91, 143901 (2003). [CrossRef] [PubMed]
  12. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005). [CrossRef] [PubMed]
  13. F. López-Tejeira, F. J. García-Vidal, and L. Martín-Moreno, “Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces,” Phys. Rev. B 72, 161405 (2005). [CrossRef]
  14. P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. Lett. 95, 263902 (2005). [CrossRef]
  15. Y. S. Jung, J. Wuenschell, T. Schmidt, and H. K. Kim, “Near-to far-field imaging of free-space and surface-bound waves emanating from a metal nanoslit,” Appl. Phys. Lett. 92, 023104 (2008). [CrossRef]
  16. H. W. Kihm, K. G. Lee, D. S. Kim, J. H. Kang, and Q.-H . Park, “Control of surface plasmon generation efficiency by slit-width tuning,” Appl. Phys. Lett. 92, 051115 (2008). [CrossRef]
  17. K. G. Lee, H. W. Kihm, J. E. Kihm, W. J. Choi, H. Kim, C. Ropers, D. J. Park, Y. C. Yoon, S. B. Choi, D. H. Woo, J. Kim, B. Lee, Q. H. Park, C. Lienau, and D. S. Kim, “Vector field microscopic imaging of light,” Nat. Photonics 1, 53–56 (2007). [CrossRef]
  18. H. W. Kihm, K. G. Lee, D. S. Kim, and K. J. Ahn, “Dual mode near-field scanning optical microscopy for near-field imaging of surface plasmon polariton,” Opt. Commun. 282, 2442–2445 (2009). [CrossRef]
  19. K. G. Lee, K. J. Ahn, H. W. Kihm, J. S. Ahn, T. K. Kim, S. Hong, Z. H. Kim, and D. S. Kim, “Surface plasmon polariton detection discriminating the polarization reversal image dipole effects,” Opt. Express 16, 10641–10649 (2008). [CrossRef] [PubMed]
  20. H. W. Kihm, J. H. Kang, J. S. Kyoung, K. G. Lee, M. A. Seo, and K. J. Ahn, “Separation of surface plasmon polariton from nonconfined cylindrical wave launched from single slits,” Appl. Phys. Lett. 94, 141102 (2009). [CrossRef]
  21. Y. Gravel, and Y. Sheng, “Rigorous solution for the transient surface plasmon polariton launched by subwavelength slit scattering,” Opt. Express 16, 21903 (2008). [CrossRef] [PubMed]
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