Optical field enhancement of nanometer-sized gaps at near-infrared frequencies

Jae Sung Ahn; Taehee Kang; Dilip K. Singh; Young-Mi Bahk; Hyunhwa Lee; Soo Bong Choi; Dai-Sik Kim

doi:10.1364/OE.23.004897

1. Introduction

Strong field enhancement on nanometer junctions has attracted much attention because of its possible applications in sensing [1–4], surface enhanced spectroscopy [5–9], molecular electronics [10–12] and high harmonic generation [13–17]. To demonstrate extremely strong field enhancement, various metallic nanostructures that have nanometer feature size – gaps [18, 19], slits [20–22], particles [10, 11, 23–25], tips [26] and combination of these structures [27] – have been proposed. Several researches show that electromagnetic field inside nanometer junction is more enhanced as the junction shrinks until the junction size reaches the quantum tunneling regime [22, 28, 29].

Despite of experimental demonstration and theoretical simulation of field enhancement on nanometer junctions, experimental quantification of the field enhancement factor still remains challenging [30, 31]. It is because of huge background in transmission and limited accessibility to single nanometer junctions. Recently, field enhancement factor of nanometer-sized dielectric gap at terahertz frequencies was quantified by measuring transmission of terahertz waves through the array of the nanometer-sized gaps [32]. In this research, the nanometer gaps extend uniformly along a millimeter-scale in opaque metal film, which successfully excludes background of illumination light. However, at shorter wavelength where the absolute permittivity of metal is of the order of 10-100, non-negligible transmission on metal film hinders exact quantification of the field enhancement factor with conventional far-field transmission measurement.

In this paper, we show near-field and far-field measurements of transmission through nanometer-sized gaps at near-infrared frequencies. In the far-field measurements, we excluded direct transmission on the metal film surface via interferometric method. Kirchhoff integral formalism was used to relate the far-field intensity to the electric field at the nanogaps [33–35]. We also used near-field scanning optical microscopy to measure field enhancements of nanogaps. Field enhancement factors quantified from the far-field measurements and the near-field measurements are consistent. By comparison with the field enhancement factors in the terahertz regime, we found the field enhancement factors in the near-infrared regime are larger than the predicted value from perfect electric conductor model. It is reported that strong confinement of surface plasmon in nanogaps leads to enhancement the electromagnetic field intensity in the gap [36, 37]. We attribute the larger field enhancement factors at near-infrared frequencies to gap plasmon resonance of our nanogap samples.

2. Experimental results and discussions

2.1. Sample fabrication

We fabricated nanogap structures by atomic layer deposition (ALD) method followed by lithography techniques of gold metal film [32]. First, we etched the array of 25 μm by 25 μm square pattern on a gold film (200 nm thickness) using photo lithography technique. Thin atomic layer of alumina (Al₂O₃) with a thickness ranging from 1 nm to 10 nm coated over patterned metal surface via ALD method. Subsequent gold layer of same thickness to the first gold film was evaporated on the alumina layer. Then, the protruded part of second gold layer was peeled of using an adhesive tape. In result, we fabricated vertically aligned nanogaps consist of alumina (Al₂O₃) sandwiched between two metal layer (Fig. 1(a)). Figure 1(b) depicts top view and cross-section view of scanning electron microscopy (SEM) image of a nanogap structure. In Fig. 1(c), higher resolution cross-sectional image taken on transmission electron microscopy (TEM) verifies the thickness of the nanogaps in atomic scale. From transmitted optical microscopy image (Fig. 1(d)), we could confirm the uniformity of the nanogap over millimeter scale.

Fig. 1 (a) Schematic of the nanogap sample. (b) Scanning Electron Microscopy (SEM) image of a nanogap sample (top-view). The inset shows cross-section view of the nanogap sample. (c) Cross-sectional Transmission Electron Microscopy (TEM) image of a nanogap sample. Bright areas correspond to Al₂O₃ layer and dark areas correspond to Au atoms. (Scale bar: 5 nm). (d) Transmitted optical microscopy image of a nanogap sample (array of 25 μm by 25 μm square pattern).

Download Full Size | PDF

2.2. Far-field measurement

Since the amount of transmitted light through the nanometer-sized gap is comparable to the amount of transmitted light through bare metal film, it is difficult to estimate electric field at the gap from conventional far-field transmission measurements. It is essential to exclude the transmitted light through the metal film from the total transmitted light. For the exclusion of the transmission on the metal film, we measured relative phase of the electric field at the gap to the electric field at the metal film using interferometry method. Figure 2(a) shows the schematics of the far-field measurement setup based on interferometry. The incident beam (Ti:sapphire mode-locked femtosecond laser, λ = 800 nm) is split by a polarizing beam splitter into two arms and one of the beams is sent through variable delay stage to adjust optical path length. After one of the beams transmitted through the sample, two beams recombine to construct their interference images.

Fig. 2 (a) Schematics of the far-field measurement setup based on interferometry. (b) Far-field optical image of a nanogap sample (red solid rectangle: gap, green dotted rectangle: metal film). (c) Reconstructed phase map of the nanogap sample from the stacked far-field images. (d) Overall transmission of the nanogap samples and bare gold film. (e) The averaged intensity from the gap region and the metal film region recorded with varying the relative phase of two beams of the interferometer. (θ: relative phase of the electric field between the transmitted light through the nanogap and the transmitted light through the metal film) (f) Field enhancement factor of nanogap samples (w = 1, 2, 5, 10 nm) deduced from far-field transmission measurement.

Download Full Size | PDF

Figure 2(b) shows far-field transmission image of a nanogap sample. Bright vertical lines correspond to the transmitted light through the nanogaps. We recorded the time averaged intensity on each pixel of the far-field image by changing the relative phase between the two incident beams. From the stacked images, the phase of the transmitted light on each pixel was determined. The phase mapping result is depicted on Fig. 2(c). There is significant phase difference (θ) between the transmitted light through the nanogaps and the transmitted light through the metal film. For closer look on the phase information, we divided the far-field image into two sections – gap region and metal film region – and averaged the intensity of the transmitted light within each section by changing the relative phase between the two incident beams. In Fig. 2(e), the averaged intensity of the gap region and the metal film region is displayed at several optical delay positions. Even though, the modulation of the averaged intensity of the metal film region is noisy, we could determine the relative phase between the transmitted light through the gap region and the transmitted light through the metal film region.

The Kirchhoff integral formalism is useful for studying electric field enhancement from subwavelength structures, since it relates the far-field electric field amplitude to the electric near-field amplitude in that structures. For an aperture on a plane metal screen, the diffracted electric field at observation point located far from the aperture is given by the Kirchhoff integral,

\vec{E} (\vec{r}) = \frac{i}{2 π r} e^{i k r} \vec{k} \times \int_{A p e r t u r e} \hat{n} \times \vec{E} (\vec{r^{'}}) e^{- i \vec{k} \cdot \vec{r^{'}}} d a^{'}

where

r

is the distance from the center of the aperture to the observation point,

\hat{n}

is the normal unit vector to the metal screen and

\vec{k}

is the wavevector of the light in the direction of observation point. Considering that the detector is placed normal to the nanogap, we defined the transmission on the nanogap sample (

T_{s a m p l e}

) and the bare metal film (

T_{d}

) by

\begin{array}{l} T_{d} = {| \frac{k \times \int_{A} \hat{n} \times E_{d i r e c t} d a^{'}}{k \times \int_{A} \hat{n} \times E_{0} d a^{'}} |}^{2} = {| \frac{E_{d i r e c t}}{E_{0}} |}^{2} \equiv {| E_{d} |}^{2}, \\ T_{s a m p l e} = {| \frac{k \times \int_{A_{1}} \hat{n} \times E_{d i r e c t} e^{i θ} d a^{'} + k \times \int_{A_{2}} \hat{n} \times E_{g a p} d a^{'}}{k \times \int_{A} \hat{n} \times E_{0} d a^{'}} |}^{2} = {| \frac{A_{1} E_{d i r e c t} e^{i θ} + A_{2} E_{g a p}}{A E_{0}} |}^{2} \\ \equiv {| E_{d} e^{i θ} + β E_{g} |}^{2} \end{array}

where

E_{d i r e c t}

is the electric field amplitude at the bare metal film surface,

E_{g a p}

is the electric field amplitude at the nanogap,

E_{0}

is the incident electric field amplitude,

θ

is the relative phase between the transmitted electric field through the nanogap and the transmitted electric field through the metal film,

k

is the wavevector of the incident light,

\hat{n}

is the unit normal vector to the sample surface,

A (= A_{1} + A_{2})

represents the total area where Kirchhoff integral is defined,

A_{1}

is the area of the metal film,

A_{2}

is the area of the nanogaps and

β = \frac{A_{2}}{A}

is the coverage ratio of the nanogaps to the whole sample. Then, the field enhancement factor (

E_{g}

) at the nanogaps can be expressed by the transmission on the reference sample (bare metal film) (

T_{d}

), the transmission on the nanogaps (

T_{s a m p l e}

), the relative phase (

θ

) determined from the interferometry and the coverage ratio (

β

).

E_{g} = \frac{1}{β} (\sqrt{T_{s a m p l e} - T_{d} \sin^{2} θ} - \sqrt{T_{d} \cos^{2} θ})

We computed the field enhancement factor at the nanogaps by substituting the measurement data to Eq. (3) (Fig. 2(f)). The ambiguity of the field enhancement factor from the far-field measurement originates from the variation of the phase of transmitted light through the metal film.

2.3. Near-field measurement & theoretical calculation

In the near-field measurements, Ti:sapphire mode-locked femtosecond laser (λ = 800 nm) illuminated from the back-side of the sample and the aperture probe gathered transmitted light through the sample. We used near-field scanning optical microscopy (NSOM) in the collection geometry [38]. The distance between the apertured probe and the sample surface was regulated by shear-force feedback within 5 nm. As the probe raster scanned over the sample surface, optical near-field intensity recorded by photodetector (SPCM-AQR-16, PerkinElmer) coupled to the fiber probe. For the normalization of transmitted light to the incident light, we measured the transmission through the bare substrate with attenuated intensity of light and used this data as a reference. The near-field probes were prepared in the following procedures: (i) tapering optical fibers by fusion splicing with CO₂ laser pulling machine (P-2000, Shutter Instrument), (ii) coating with aluminum layer (100 nm thickness) with chromium sticking layer (5 nm thickness) on the tapered optical fiber using evaporation apparatus, (iii) formation of apertures on the apex of the metal-coated fibers by slicing the probes from side direction using focused ion beam (FIB) milling machine (Quanta 3D, FEI). For uniform metal coating we used tilted fiber mount and rotated the probes during the evaporation. The diameter of aperture of fabricated probes was determined by the position of slicing. The probes processed by FIB milling have flat bottom surface, which exploit the strong confinement of the optical near-field [39].

We scanned over single nanogap structures with varying the gap size from 1 nm to 10 nm. Figure 3(a) shows near-field optical image of 1 nm width gap sample obtained from NSOM scanning on 5 μm by 5 μm area. The fringe pattern at the proximity of the nanogap comes from the interference of the transmitted light through the metal film and surface plasmon at air/metal interface. We observed the variation of the transmitted intensities of light through the nanogap and attributed this variation to the deviation of the gap widths from its target values. We measured the cross-sectional profiles of the near-field intensity to the perpendicular direction to the gap axis (Fig. 3(b)). By averaging all the cross-sectional profiles, the sharp resonances of the field enhancement factors in theoretical calculation (Fig. 4(c)) were suppressed. It is because that the resonance, comes from the width of the nanogap and from the thickness of the nanogap sample (explained later), was mitigated on the averaging process of the near-field profiles. For the reference measurement, we replaced the sample to the bare glass substrate and attenuated the illumination intensity by the amount of transmission coefficient of the metal film. The field enhancement factors from the near-field measurements were determined from the Kirchhoff formalism, similar to the far-field estimation but including the effect of transmission through the subwavelength hole (NSOM aperture). In this case, the field enhancement factors can be calculated by

(f i e l d e n h a n c e m e n t) \equiv (\frac{E_{g a p}}{E_{0}}) ≃ 4 (\frac{a}{λ}) (\frac{a}{w}) \frac{\sqrt{I_{t}}}{\sqrt{I_{r e f}}}

where

\sqrt{I_{t}} / \sqrt{I_{r e f}}

is the ratio of the averaged near-field peak amplitude (

\sqrt{I_{t}}

) to the averaged field amplitude of the reference sample (

\sqrt{I_{r e f}}

),

(w / a)

is the geometrical coverage ratio and

(4 a / λ)

is the circular subwavelength aperture transmission factor. Figure 3(c) shows field enhancement factors of the nanogaps of varying width from 1 nm to 10 nm at 800 nm wavelength. They are consistent to the field enhancement factors estimated from the far-field measurements. The error bars come from the variation of the near-field peak intensities from the averaged peak value.

Fig. 3 (a) Near-field optical image of a nanogap sample (gap size: 1 nm). (b) Cross-section profile of the near-field intensity along the perpendicular direction to the axis of the nanogap. Gap size (w) varies from 1 nm to 10 nm (w = 1, 2, 5, 10 nm) (c) Field enhancement factor deduced from the near-field measurements (black squares with error bar).

Download Full Size | PDF

Fig. 4 (a) Schematic illustration and geometry of the nanogap structure in our calculation (b) Contour plot of calculated near-field distribution of the nanogap structure. Gap size (w) varies from 1 nm to 10 nm (w = 1, 2, 5, 10 nm). The rectangle size of each contour plot depicts 40 nm x 40 nm area. (c) Calculation of the field enhancement factor of the nanogaps for different metal thickness.

Download Full Size | PDF

To check the validity for the measurement of field enhancement factor, we calculated the electromagnetic field distribution on the surface of the nanogap based on coupled mode theory and surface impedance boundary conditions [40]. The coupled mode theory is a kind of modal expansion method, which is used to analyze the transmission properties of subwavelength periodic structures. In this theory, electromagnetic fields are expanded by the eigenmodes of each region (top and bottom of the metal film and inside the nanogap). The parallel components of the electric and magnetic fields at the two interfaces (top and bottom of the metal film) are determined by matching boundary conditions. However, the metal is normally treated as a perfect electrical conductor in the coupled mode theory. In this paper, we applied the surface impedance boundary conditions to introduce the finite dielectric constant of metals at optical frequencies. For examples, the electric and magnetic fields expanded by plane wave modes satisfying Helmholtz equation in transmitted region are written as

\begin{array}{l} H_{y}^{} = \sqrt{\frac{ε_{0}}{μ_{0}}} \sum_{n = - \infty}^{\infty} [T_{n} e^{- i k_{z}^{n} (z + \frac{h}{2})} e^{i k_{x}^{n} x}] \\ E_{x}^{} = \frac{i}{k_{0} ε_{a i r}} \sqrt{\frac{μ_{0}}{ε_{0}}} (\frac{\partial H_{z}}{\partial y} - \frac{\partial H_{y}}{\partial z}) = \frac{i}{k_{0} ε_{a i r}} \sum_{n} [- i k_{z}^{n} T_{n} e^{- i k_{z}^{n} (z + \frac{h}{2})} e^{i k_{x}^{n} x}] \\ E_{z}^{} = \frac{i}{k_{0} ε_{a i r}} \sqrt{\frac{μ_{0}}{ε_{0}}} (\frac{\partial H_{y}}{\partial x} - \frac{\partial H_{x}}{\partial y}) = \frac{i}{k_{0} ε_{a i r}} \sum_{n} [i k_{x}^{n} T_{n} e^{- i k_{z}^{n} (z + \frac{h}{2})} e^{i k_{x}^{n} x}] \end{array}

where

h

is the thickness of the nanogap sample,

n

is the mode number,

k_{x}^{n} = k_{0 x}^{} + \frac{2 π n}{d}

and

k_{z}^{n} = \pm \sqrt{ε_{a i r} k_{0}^{2} - {(k_{x}^{n})}^{2}}

are horizontal and vertical components of

k

vectors for each plane wave modes,

d

is the period of the nanogaps,

T_{n}

is the unknown complex mode amplitude for transmitted waves, respectively. We plotted the contour plot of the calculated electric field at the nanogap (Fig. 4(b)). We ascertained that the electric field is strongly confined within 100 nm range for all the nanogaps. Therefore, most of radiations from the nanogaps are collected by the near-field probe (aperture diameter ~150 nm) [41].

As the gap size decreases, field enhancement factors increase much drastically. The same tendency was shown on Fabry-Pérot resonance of gap plasmon for nanoslits on a metal film [36, 37]. This resonance is shown in our calculation at 1.8 nm and 5 nm for 200 nm metal thickness case in Fig. 4(c), and this resonance peaks vary as the thickness changed, which describes the behavior of the Fabry-Pérot type resonance. However, in our nanogap sample, deviation from ideal structure suppresses the resonance. For examples, some nanogaps slightly inclined from vertical orientation and broaden at their ends. Even though the experimental results do not perfectly match to the theoretical calculations, they are close to the theoretical calculations in the case where there is no resonance.

To this end, we measured frequency dependence of field enhancement factor of 1 nm width nanogaps at near-infrared frequencies. The optical cavity of Ti:sapphire mode-locked laser which illuminates the nanogap samples tuned to have broadband output (740~820 nm). We scanned over the nanogap sample surface along the perpendicular direction to the gap axis and took the transmission spectrum at every pixels using a near-field optical microscopy coupled to spectrometer (Monochromator: Andor Shamrock 303i, Detector: Andor iXon Ultra 897). Figure 5(a) shows the transmission spectra from the near-field measurements of the nanogap samples. The white dotted line corresponds to the position of the nanogap. We analyzed the transmission spectra to estimate field enhancement over the whole spectrum of the illumination source. We plotted the field enhancement factors of 1 nm width nanogap from 370 THz to 410 THz frequency (Fig. 5(b)). The error bar in the plot originates from the variation of near-field intensities. Due to low intensity of the illumination source at <380 THz frequencies, the field enhancement factors at this range were underestimated. The field enhancement factors of 1 nm width nanogap are larger than five over the whole range of Fig. 5(b).

Fig. 5 (a) Transmission spectra of a nanogap sample (w = 1 nm) taken at every pixel along the perpendicular direction to the gap axis. The white dotted line corresponds to position of the gap. (b) Field enhancement factor at near-infrared frequencies. (c) Field enhancement factor from THz frequencies to optical frequencies. Dotted line is 1/f fitting of field enhancement. Because of resonant cavity mode of our nanogap sample at near-infrared frequencies, field enhancement factor is 10 times larger than the fitted value.

Download Full Size | PDF

To put the moderate field enhancement of five near wavelength of 800 nm into perspective, we compared the field enhancement factors of the 1 nm width gap in the terahertz regime and the near-infrared regime in Fig. 5(c). The field enhancement factors in the terahertz regime (the black dots on Fig. 5(c)) were measured by the terahertz transmission measurement of a nanogap sample (5 mm in length, 200 nm in thickness) using terahertz time-domain spectroscopy technique. The field enhancement essentially originates from the capacitive charging of the nanogap by the magnetic-field induced surface currents, which inevitably leads to the 1/f dependence (dotted line). However, at the near-infrared regime, the field enhancement factors are larger, by one order of magnitude, than the simple capacitive charging prediction. We contend that this stronger enhancement comes from the gap plasmon resonance, also included in our theoretical calculation results, of metal-insulator-metal (MIM) waveguide in our nanogap sample at near-infrared frequencies.

3. Conclusion

In conclusion, we measured transmission through nanometer gaps at near-infrared frequencies and quantified field enhancement factors inside the nanometer gaps from the far-field and near-field measurements. From the transmission measurements, we quantified field enhancement factors of the nanometer gaps at near-infrared frequencies. We thought the gap plasmon resonance is the reason of the stronger field enhancement of the nanogaps at near-infrared frequencies. We believe that our nanogap structure has advantages on the quantification of the field enhancement factors because of its low background in transmission. In addition, near-field measurements have advantages of low background and accessibility to a single nanostructure. Hence, we expect the combination of the nanogap structure and near-field scanning optical microscopy will pave the way to inspect optical phenomena in atomic scale and to develop quantum plasmonic devices.

Acknowledgments

The authors would like to thank Joonyeon Kim, Jiyeah Rhie and Jeeyoon Jeong for their contributions to fabrication of the nanogap samples. This work was supported by the National Research Foundation of Korea [NRF] grant funded by the Korea government (MSIP) (NRF-2005-0093838, NRF-2008-00580, NRF-2008-0061906, NRF-2014R1A2A2A01006378).

References and links

1. P. K. Jain and M. A. El-Sayed, “Plasmonic coupling in noble metal nanostructures,” Chem. Phys. Lett. 487(4-6), 153–164 (2010). [CrossRef]

2. D. K. Lim, K. S. Jeon, J. H. Hwang, H. Kim, S. Kwon, Y. D. Suh, and J. M. Nam, “Highly uniform and reproducible surface-enhanced Raman scattering from DNA-tailorable nanoparticles with 1-nm interior gap,” Nat. Nanotechnol. 6(7), 452–460 (2011). [CrossRef] [PubMed]

3. H.-R. Park, K. J. Ahn, S. Han, Y.-M. Bahk, N. Park, and D.-S. Kim, “Colossal absorption of molecules inside single terahertz nanoantennas,” Nano Lett. 13(4), 1782–1786 (2013). [PubMed]

4. Z. Fang, Z. Liu, Y. Wang, P. M. Ajayan, P. Nordlander, and N. J. Halas, “Graphene-antenna sandwich photodetector,” Nano Lett. 12(7), 3808–3813 (2012). [CrossRef] [PubMed]

5. P. L. Stiles, J. A. Dieringer, N. C. Shah, and R. P. Van Duyne, “Surface-enhanced raman spectroscopy,” Annu Rev Anal. Chem. (Palo Alto Calif.) 1(1), 601–626 (2008). [CrossRef] [PubMed]

6. A. Gopinath, S. V. Boriskina, B. M. Reinhard, and L. Dal Negro, “Deterministic aperiodic arrays of metal nanoparticles for surface-enhanced Raman scattering (SERS),” Opt. Express 17(5), 3741–3753 (2009). [PubMed]

7. S. Roh, T. Chung, and B. Lee, “Overview of the characteristics of micro- and nano-structured surface plasmon resonance sensors,” Sensors (Basel) 11(12), 1565–1588 (2011). [CrossRef] [PubMed]

8. A. Berrier, P. Albella, M. A. Poyli, R. Ulbricht, M. Bonn, J. Aizpurua, and J. G. Rivas, “Detection of deep-subwavelength dielectric layers at terahertz frequencies using semiconductor plasmonic resonators,” Opt. Express 20(5), 5052–5060 (2012). [CrossRef] [PubMed]

9. P. Alonso-González, P. Albella, M. Schnell, J. Chen, F. Huth, A. García-Etxarri, F. Casanova, F. Golmar, L. Arzubiaga, L. E. Hueso, J. Aizpurua, and R. Hillenbrand, “Resolving the electromagnetic mechanism of surface-enhanced light scattering at single hot spots,” Nat. Commun. 3, 684 (2012). [CrossRef] [PubMed]

10. P. Nordlander, “Applied physics. molecular tuning of quantum plasmon resonances,” Science 343(6178), 1444–1445 (2014). [CrossRef] [PubMed]

11. S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014). [CrossRef] [PubMed]

12. M. Galperin and A. Nitzan, “Molecular optoelectronics: the interaction of molecular conduction junctions with light,” Phys. Chem. Chem. Phys. 14(26), 9421–9438 (2012). [CrossRef] [PubMed]

13. H. Merbold, A. Bitzer, and T. Feurer, “Second harmonic generation based on strong field enhancement in nanostructured THz materials,” Opt. Express 19(8), 7262–7273 (2011). [PubMed]

14. D. Bar-Lev and J. Scheuer, “Efficient second harmonic generation using nonlinear substrates patterned by nano-antenna arrays,” Opt. Express 21(24), 29165–29178 (2013). [CrossRef] [PubMed]

15. G. F. Walsh and L. Dal Negro, “Enhanced second harmonic generation by photonic-plasmonic fano-type coupling in nanoplasmonic arrays,” Nano Lett. 13(7), 3111–3117 (2013). [CrossRef] [PubMed]

16. S. Palomba, M. Danckwerts, and L. Novotny, “Nonlinear plasmonics with gold nanoparticle antennas,” J. Opt A Pure Appl. Opt. 11, 6–9 (2009).

17. M. R. Singh, “Enhancement of the second-harmonic generation in a quantum dot-metallic nanoparticle hybrid system,” Nanotechnology 24(12), 125701 (2013). [CrossRef] [PubMed]

18. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96(9), 097401 (2006). [CrossRef] [PubMed]

19. D. R. Ward, F. Hüser, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5(10), 732–736 (2010). [CrossRef] [PubMed]

20. F. J. Garcia-Vidal, L. Martin-Moreno, T. W. Ebbesen, and L. Kuipers, “Light passing through subwavelength apertures,” Rev. Mod. Phys. 82(1), 729–787 (2010). [CrossRef]

21. Y. Xie, A. Zakharian, J. Moloney, and M. Mansuripur, “Transmission of light through slit apertures in metallic films,” Opt. Express 12(25), 6106–6121 (2004). [CrossRef] [PubMed]

22. M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009). [CrossRef]

23. J. A. Scholl, A. García-Etxarri, A. L. Koh, and J. A. Dionne, “Observation of quantum tunneling between two plasmonic nanoparticles,” Nano Lett. 13(2), 564–569 (2013). [CrossRef] [PubMed]

24. J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483(7390), 421–427 (2012). [CrossRef] [PubMed]

25. Y. Tanaka, A. Sanada, and K. Sasaki, “Nanoscale interference patterns of gap-mode multipolar plasmonic fields,” Sci. Rep. 2, 764 (2012). [CrossRef] [PubMed]

26. K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491(7425), 574–577 (2012). [CrossRef] [PubMed]

27. C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012). [CrossRef] [PubMed]

28. R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3, 825 (2012). [CrossRef] [PubMed]

29. J. Zuloaga, E. Prodan, and P. Nordlander, “quantum description of the plasmon resonances of a nanoparticle dimer,” Nano Lett. 9(2), 887–891 (2009). [CrossRef] [PubMed]

30. S. Mubeen, S. Zhang, N. Kim, S. Lee, S. Krämer, H. Xu, and M. Moskovits, “Plasmonic properties of gold nanoparticles separated from a gold mirror by an ultrathin oxide,” Nano Lett. 12(4), 2088–2094 (2012). [CrossRef] [PubMed]

31. Y. Fang, N.-H. Seong, and D. D. Dlott, “Measurement of the distribution of site enhancements in surface-enhanced Raman scattering,” Science 321(5887), 388–392 (2008). [CrossRef] [PubMed]

32. X. Chen, H. R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D. S. Kim, and S. H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electromagnetic waves,” Nat. Commun. 4, 2361 (2013). [CrossRef] [PubMed]

33. J. S. Kyoung, M. A. Seo, H. R. Park, K. J. Ahn, and D. S. Kim, “Far field detection of terahertz near field enhancement of sub-wavelength slits using Kirchhoff integral formalism,” Opt. Commun. 283(24), 4907–4910 (2010). [CrossRef]

34. F. Moreno, P. Albella, and M. Nieto-Vesperinas, “Analysis of the spectral behavior of localized plasmon resonances in the near- and far-field regimes,” Langmuir 29(22), 6715–6721 (2013). [CrossRef] [PubMed]

35. P. Alonso-González, P. Albella, F. Neubrech, C. Huck, J. Chen, F. Golmar, F. Casanova, L. E. Hueso, A. Pucci, J. Aizpurua, and R. Hillenbrand, “Experimental verification of the spectral shift between near- and far-field peak intensities of plasmonic infrared nanoantennas,” Phys. Rev. Lett. 110(20), 203902 (2013). [CrossRef] [PubMed]

36. Q. Cao and P. Lalanne, “Negative role of surface plasmons in the transmission of metallic gratings with very narrow slits,” Phys. Rev. Lett. 88(5), 057403 (2002). [CrossRef] [PubMed]

37. K.-L. Lee, W.-S. Wang, and P.-K. Wei, “Sensitive label-free biosensors by using gap plasmons in gold nanoslits,” Biosens. Bioelectron. 24(2), 210–215 (2008). [CrossRef] [PubMed]

38. E. Betzig, M. Isaacson, and A. Lewis, “Collection mode near‐field scanning optical microscopy,” Appl. Phys. Lett. 51(25), 2088–2090 (1987). [CrossRef]

39. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2012).

40. H. Lochbihler and R. A. Depine, “Properties of TM resonances on metallic slit gratings,” Appl. Opt. 51(11), 1729–1741 (2012). [CrossRef] [PubMed]

41. T. Iida, Y. Aiba, and H. Ishihara, “Anomalous optical selection rule of an organic molecule controlled by extremely localized light field,” Appl. Phys. Lett. 98(5), 053108 (2011). [CrossRef]

Optical field enhancement of nanometer-sized gaps at near-infrared frequencies

Abstract

1. Introduction

2. Experimental results and discussions

2.1. Sample fabrication

2.2. Far-field measurement

2.3. Near-field measurement & theoretical calculation

3. Conclusion

Acknowledgments

References and links

Cited By

Figures (5)

Equations (5)

Optics Express