Fractal shaped structures formed with a 100-nm-period square lattice of gold nanoparticles placed on a gold film are characterized by using far-field nonlinear scanning optical microscopy, in which two-photon photoluminescence (TPL) excited with a strongly focused laser beam (in the wavelength range of 730 – 790 nm) is detected. The TPL images recorded for all wavelengths exhibit diffraction-limited (~ 0.6 μm) bright spots corresponding to the field intensity enhancement of up to 150, whose positions are dictated by the incident light wavelength and polarization. We relate these field enhancements to the occurrence of constructive interference of surface plasmons (SPs), which are excited by the incident radiation (due to scattering by nanoparticles) and partially reflected by fractal shaped boundaries due to a difference in the SP effective index at a flat and periodically corrugated gold surface. The conjecture on SP index difference is verified with observations (using leakage radiation microscopy) of SP focusing by circular and waveguiding by rectangular areas filled with periodically arranged nanoparticles.
©2007 Optical Society of America
Electromagnetic interactions in nanostructured materials and nanostructures give rise to various fascinating optical phenomena occurring at nanoscale. One of the main research directions in nano-optics is the search for configurations that efficiently interconvert propagating (μm-sized) and strongly localized (nm-sized) optical fields resulting thereby in strongly enhanced local fields, which are indispensable for optical characterization, sensing and manipulation at nanoscale . Various strategies have been suggested and pursued in order to realize a strong and robust field enhancement effect. Resonant interactions in metal nanostructures involving both localized and propagating surface plasmons (SPs) have been intensively and extensively investigated using nanostructures of different shapes and configurations, ranging from individual pointed particles [2,3] to their pairs [4–6] and periodic  and random [8,9] ensembles. Insofar these structures represented either well-defined regular configurations exhibiting resonant field enhancements at one or several wavelengths [3–7] or irregular random nanostructures featuring (spatially separated) resonant excitations covering a wide spectrum range [8,9]. While the former structures offer the possibility for dedicated design, the latter might be very attractive for specific applications requiring resonant responses in a broad wavelength range, e.g., for multi-channel sensing and manipulation at nanoscale.
Two-photon photoluminescence (TPL) from metals was previously described [10,11], with spatially resolved TPL studies  and near-field imaging  being lately used for characterization of local field enhancement. Here we report investigations of field enhancement effects in fractal shaped metal structures fabricated using the electron-beam lithography (EBL) that are formed with a regular (100-nm-period) lattice of gold nanoparticles placed on a gold film and characterized by using far-field nonlinear scanning optical microscopy, in which TPL excited with a strongly focused laser beam is detected . By design the fabricated structures consist of periodic nanoparticle arrays of practically all possible shapes within the available spatial range (from 100 nm to 100 μm), so that one would expect to observe resonant field enhancements in a broad wavelength range.
Our experimental setup for TPL microscopy is schematically shown in Fig. 1 and essentially the same as that used in the previous experiments [9,14]. It consists of a scanning optical microscope in reflection geometry built on the base of a commercial microscope and a computer-controlled two-dimensional piezoelectric translation stage (steps down to 50 nm, accuracy ~4 nm). The linearly polarized light beam from a mode-locked pulsed (pulse duration ~200 fs, repetition rate ~80 MHz) Ti-Sapphire laser (λ = 730–790 nm, δλ ~ 10 nm, average power ~300 mW) is used as a source of sample illumination at the fundamental harmonic (FH) frequency. After passing an optical isolator (to avoid back-reflection), half-wave plate, polarizer and wavelength selective beam splitter, the laser beam is focused on the sample surface at normal incidence with a Mitutoyo infinity-corrected ×100 objective. The illumination power was selected in the range 1.2 – 3.6 mW depending on wavelength and the obtained TPL signals. The TPL radiation generated in reflection and the reflected FH beam are collected with the same objective, separated by the beam splitter, directed through the appropriate filters and polarizers and detected with two photomultiplier tubes, the tube for TPL photons being connected with a photon counter. The TPL detection has been improved as compared to that used in our previous investigations [9,14] leading to very low TPL dark counts, typically ~ 20 counts per second (cps). Both TPL and FH signals are simultaneously recorded as a function of the scanning coordinate resulting in the matching TPL and FH images of the sample surface. The FH and TPL resolution at full width half maximum is approximately ~ 0.8 μm and ~ 0.6 μm, respectively.
The sample fabricated with the EBL followed by liftoff consists of round gold particles (height ~ 50 nm) arranged periodically within fractal shaped regions positioned on a smooth ~ 50-nm-thick gold film. For each fractal pattern, spatial locations of nanoparticles were calculated so as to form a 100-nm-period square lattice filling the inner region of the same (small) part of the Mandelbrot fractal  extending over ~ 100 × 100 μm2. The same fractal pattern formed by gold nanoparticles of different diameter (40, 50, 60 and 70 nm) was fabricated on different places on the gold film surface. It should be emphasized that the idea was to fabricate well defined fractal nanostructures, being in contrast to the previous EBL-fabricated random nanostructures [9,14], for which proximity effects in the EBL process were found extremely important resulting in uncontrollable melting together of individual nanoparticles.
Geometry of the entire fractal structure defined for the EBL and a scanning electron microscopy (SEM) image obtained for the fabricated structure formed by 50-nm-diameter particles are shown in Fig. 2(a, b). The quality of fabricated fractal nanostructures was evaluated by comparing SEM images with the designed geometry. It turned out that the fractal structures formed by 70-nm-diameter particles were irregular with individual nanoparticles being often melted together due to proximity effects, whereas those formed by 40-nmdiameter particles had many particles missing due to liftoff. The fractal structure consisting of 50-nm-diameter particles exhibited quite a few missing particles as well. However, the structure formed by 60-nm-diameter particles had very few particles missing [cf. Fig. 2(c) and 2(d)] and was therefore chosen for detailed characterization with the TPL microscopy. Notice the self-similarity of the fractal structure [cf. Fig. 2(a) and 2(c)] featuring nanoparticle clusters of practically all possible shapes within the available spatial range (from 100 nm to 100 μm).
Typical FH and TPL images obtained at an excitation wavelength of 730 nm with the fractal structure formed by 60-nm-diameter particles are shown in Fig. 2(e, f). It is seen that the FH image obtained in the cross-polarized configuration [Fig. 2(e)] replicates well (with the diffraction-limited resolution) the shape of fractal structure shown with the SEM image [Fig. 2(b)]. The center fractal areas having the largest density of nanoparticles exhibit the strongest (de-polarized) scattering and appear brighter in the FH image. On the other hand, the TPL image [Fig. 2(f)] only weakly indicates the fractal shape displaying instead several bright spots distributed inside the fractal structure in a fashion which is somewhat similar to that observed with random gold nanostructures [9,14]. It should be noted that, for an incident power of less than 1.2 mW, the maximum TPL signal was measured being close to ~12 × 103 cps, which is one order of magnitude larger than that obtained with the random gold nanostructures [9,14].
The FH images recorded in the course of our investigations have been obtained in the cross-polarized detection configuration [see, e.g. Fig. 2(e)]. Note that small gold particles placed on top of a smooth gold film can be difficult to identify using conventional microscopy due to large background reflection from smooth gold. However, by detecting the reflected radiation in the cross-polarized configuration (which is somewhat similar to observing only scattered light in dark-field microscopy) the FH image contrast can be substantially increased, reaching in our case ~ 50% and resulting thereby in clear images of the nanostructure under inspection. Sharp and detailed FH images with the (diffraction-limited) resolution of ~ 0.8 μm make it possible to precisely compare the FH and SEM images identifying accurately the locations inspected with the TPL microscopy. Since the FH and TPL images were obtained simultaneously, we could further merge the corresponding TPL and SEM images allowing for precise correlation between high resolution SEM images with the corresponding zoom in the TPL images obtained for different wavelengths and polarization configurations (Fig. 3).
Usage of TPL scanning optical microscopy for characterization of the local-field enhancement (for the incident FH radiation) in gold nanostructures can be considered well established [5–7]. Influence of the FH wavelength and polarization on the location of bright spots in the TPL images (Fig. 3) can be related to the occurrence of resonant (multiple) scattering of SPs within the structure boundaries. The SP waves (excited due to scattering of the tightly focused FH beam by nanoparticles) propagating along the surface inside a periodic array of nanoparticles experience an increase in the effective refractive index  and, for the array periods considerably smaller than the wavelength, relatively weak out-of-plane scattering . Note that a similar increase of the SP effective refractive index has been exploited for realization of fiber-accessible SP waveguides designed from two-dimensional periodic patterns of gold nanoparticles . It is then reasonable to assume that fractal shaped boundaries (in the spatial range from 100 nm to 100 μm) of the structure would partially reflect and diffract incident SPs, forming thereby cavities that could be resonant at practically any wavelength. The corresponding physics is quite similar to that found with so-called fractal drums for which high-order modes localized to very small areas occur due to constructive interference of waves reflected and diffracted by a fractal shaped boundary . In our case, the bright TPL spots can be related to spatially localized eigenmodes at the FH frequency excited via incident radiation scattering off nanoparticles. Different wavelengths and/or polarizations of the incident FH radiation lead to the excitation of different FH eigenmodes [cf. Figs. 3(a), 3(b), 3 (c) and 3(e)]. On the other hand, the TPL images obtained for different polarizations of the detected TPL radiation are, understandably, very similar [cf. Figs. 3(c) and 3(d), 3(e) and 3(f)]. Small differences can be explained by the circumstance that the TPL radiation originating from the locations of FH field enhancements (bright spots) interacts also with the immediate scattering environment that can influence the process of TPL scattering in the reflection direction (toward its detection).
Quantitative evaluation of field intensity enhancements can be carried out by comparing TPL signals from bright spots within the nanostructure to that from a smooth gold film [5–7]. Following this approach, the TPL enhancement factor α can be written down:
where TPL is the obtained TPL signal, < P > is the used average incident power, and A is the area producing the enhancement. Here Afilm is taken as the area of focused FH beam cross section, i.e. ~ π(0.4 μm)2, whereas Afrac is estimated from the area of gold nanoparticles being illuminated by the focused FH beam since the TPL signal originates primarily from nanoparticles . Using calibrated TPL signals obtained from smooth gold film regions (e.g., ~ 2.9 kcps at λ = 730 nm and the incident FH power of 25 mW), we have estimated TPL enhancement factors of up to 150 for various bright spots observed at different configurations of wavelength and polarization. However, it should be borne in mind that the (far-field) TPL images are diffraction limited so that, in fact, the TPL signals might originate (in some cases) from only a few neighbor nanoparticles. In such a case, the TPL enhancements should be estimated using much smaller values of Afrac resulting thereby in significantly larger values of α.
Finally, we have directly verified the above conjecture on SP index difference at a flat and periodically corrugated gold surface by considering the SP interaction with regularly shaped periodic arrays of nanoparticles. To this aim, we have fabricated (using the EBL) a sample having differently shaped 100-nm-period arrays of gold nanoparticles (height ~ 50 nm, diameter ~ 60 nm) placed on a smooth ~ 50-nm-thick gold film [Fig. 4(a, b)] and characterized by using leakage radiation microscopy (LRM) . The SP excitation [Fig. 4(c)] was realized by focusing a laser beam onto a 100-nm-wide gold ridge (height ~ 50 nm) fabricated in the vicinity of nanoparticle arrays . Partial refraction [Fig. 4(d)] and focusing [Fig. 4(e)] of an excited SP beam by a 7.5-μm-diameter circular array (depending on the mutual orientation of the excited SP beam and the circular structure) was observed demonstrating unambiguously that, as expected [16–18], the SP effective index is larger inside nanoparticle arrays than at a flat surface. The index difference was estimated from the focusing effect shown in Fig. 4(e) as being equal to ~ 0.1. This difference is quite sufficient to form a stripe SP waveguide though for relatively large widths [Fig. 4(f)]. Note that the obtained LRM images indicate that the fabricated structures exhibit relatively weak out-of-plane SP scattering, as expected for small particles and small (i.e., smaller than that required to realized the band-gap effects) periods . It is clear that one can think of other interesting applications of the observed effect for SP micro-optics utilizing nanoparticle arrays of various shapes.
In summary, we have used the TPL scanning optical microscopy to characterize the local field enhancements in a fractal shaped periodic structure of gold nanoparticles placed on a gold film surface. The TPL images recorded for all wavelengths was found to exhibit diffraction-limited (~ 0.6 μm) bright spots corresponding to the field intensity enhancement of up to 150, whose positions are dictated by the incident light wavelength and polarization. We have related these field enhancements to the occurrence of constructive interference of surface plasmons (SPs), which are excited by the incident radiation (due to scattering by nanoparticles) and partially reflected by fractal shaped boundaries due to a difference in the SP effective index at a flat and periodically corrugated gold surface. The occurrence of SP index difference was directly validated with LRM observations of SP focusing by circular and waveguiding by rectangular areas filled with periodically arranged nanoparticles. We believe that the usage of periodic nanoparticle arrays, which are exhibiting (for periods much smaller than the wavelength) an increase in the SP index while keeping low the out-of-plane SP scattering, can find many interesting applications depending on the array shape (circular, rectangular, fractal, single- and multi-connected etc.) within SP micro-optics, ranging from SP manipulation and guiding to SP mediated field enhancement effects. We are conducting further research in this area.
The authors gratefully acknowledge support from the European Network of Excellence, Plasmo-Nano-Devices (FP6-2002-IST-1-507879) and the NABIIT project (Contract No. 2106-05-033 from the Danish Research Agency).
References and links
1. V. M. Markel and T. F. George, eds. Optics of Nanostructured Materials, (John Wiley and Sons, New York, NY, 2001).
2. G. T. Boyd, Th. Rasing, J. R. R. Leite, and Y. R. Shen, “Local-field enhancement on rough surfaces of metals, semimetals, and semiconductors with the use of optical second-harmonic generation,” Phys. Rev. B 30, 519–526 (1984), and references therein. [CrossRef]
3. E. J. Sánchez, L. Novotny, and X. S. Xie, “Near-Field fluorescence microscopy based on two-photon excitation with metal tips,” Phys. Rev. Lett. 82, 4014–4017 (1999). [CrossRef]
4. K. Kneipp, H. Kneipp, I. Itzkan, R. R. Dasari, and M. S. Feld, “Surface-enhanced Raman scattering and biophysics,” J. Phys. Condens. Matter , 14, R597–R624 (2002). [CrossRef]
5. P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005). [CrossRef] [PubMed]
7. A. Hohenau, J. R. Krenn, S. G. Rodrigo, L. Martin-Moreno, F. Garcia-Vidal, J. Beermann, and S. I. Bozhevolnyi, “Spectroscopy and nonlinear microscopy of gold nanoparticle arrays on gold films,” Phys. Rev. B 75, 085104 (2007). [CrossRef]
8. A. K. Sarychev and V. M. Shalaev, “Electromagnetic field fluctuations and optical nonlinearities in metaldielectric composites,” Phys. Rep. 335, 275 (2000); M. I. Stockman, “Local fields’ localization and chaos and nonlinear-optical enhancement in clusters and composites,” in Optics of Nanostructured Materials, Ref. 1, p. 313, and references therein. [CrossRef]
10. A. Mooradian, “Photoluminescence of metals,” Phys. Rev. Lett. 22, 185 (1969). [CrossRef]
11. G. T. Boyd, Z. H. Yu, and Y. R. Shen, “Photoinduced luminescence from the noble metals and its enhancement on roughened surfaces,” Phys. Rev. B 33, 7923 (1986). [CrossRef]
12. M. R. Beversluis, A. Bouhelier, and L. Novotny, “Continuum generation from single gold nanostructures through near-field mediated intraband transitions,” Phys. Rev. B 68, 115433 (2003). [CrossRef]
13. A. Bouhelier, M. R. Beversluis, and L. Novotny, “Characterization of nanoplasmonic structures by locally excited photoluminescence,” Appl. Phys. Lett. 83, 5041 (2003). [CrossRef]
14. J. Beermann and S. I. Bozhevolnyi, ”Microscopy of localized second-harmonic enhancement in random metal nanostructures,” Phys. Rev. B 69, 155429 (2004). [CrossRef]
15. K. Falconer, Fractal Geometry: Mathematical Foundations and Application (John Wiley and Sons, Chichester, UK, 2003). [CrossRef]
17. T. SØndergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge gratings for long-range surface plasmon polaritons,“ Phys. Rev. B. 73, 045320 (2006). [CrossRef]
18. S. A. Maier, M. D. Friedman, P. E. Barclay, and O. Painter, “Experimental demonstration of fiberaccessible metal nanoparticle plasmon waveguides for planar energy guiding and sensing,” Appl. Phys. Lett. 86, 071103 (2005). [CrossRef]
19. C. Even, S. Russ, V. Repain, P. Pieranski, and B. Sapoval, “Localizations in fractal drums: An experimental study,” Phys. Rev. Lett. 83, 726–729 (1999). [CrossRef]
20. I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, “Surface plasmon polariton beam focusing with parabolic nanoparticle chains,” Opt. Express 15, 6576–6582 (2007). [CrossRef] [PubMed]