Abstract: We compare the plasmonic response of two complementary structures to a scanning electron probe; a silver nanowire and a nanoslot in a silver film of comparable dimensions, desirable for their localized electromagnetic enhancement and enhanced optical transmission respectively. Through electron energy loss spectroscopy, multiple plasmonic resonant harmonics setup in both structures are resolved with inverted phase, in agreement with Babinet’s principle, and of consequence in the design and fabrication of nanostructures.
©2012 Optical Society of America
Nanometallic objects derive their unique optical properties from the ability to support collective surface electron excitations, known as surface plasmons. Surface plasmons are essentially electromagnetic waves trapped at a metallic surface through their interaction with the free electrons of the metal [1,2]. By confining electromagnetic energy into sub wavelength volumes, plasmonic structures can efficiently mediate interactions between propagating radiation and nanoscale objects and devices . Of recent interest is the behavior of plasmonic excitations in both metallic nanowires and holes in metal films, responsible for localized electromagnetic enhancement  and enhanced optical transmission respectively . Such structures are finding a growing number of applications in solar cells , light-emitting diodes  and cancer treatment . Here, we compare the plasmonic response of two complementary structures to a scanning electron probe; a silver single crystalline nanowire and a nanoslot in a silver film of comparable dimensions. We image multiple plasmonic resonant harmonics setup in both structures and record their resonance energy. The first four excited resonance modes are resolved in both structures and their resonance energies are comparable, however, the spatial symmetry of the plasmonic resonances are reversed, in agreement with Babinet’s principle, imaged for the first time in a complementary set of nanoscale structures of the same size. The presence of sub wavelength size holes in an opaque metal film gives rise to a variety of interesting optical phenomena, such as enhanced optical transmission and wavelength filtering . These phenomena are now known to be due to the interaction of the light with collective electronic resonances in the surface of the metal film, which transport the photons' electromagnetic energy through the sub-wavelength holes, re-radiating it on the other side, giving the film increased transparency . Sub wavelength metallic nanowires are also known to strongly confine and radiate electromagnetic energy at the nanoscale . Due to their finite submicron length, they exhibit pronounced resonances at optical frequencies.
The efficient inter-conversion of propagating light and localized enhanced fields, achieved in both nanoslot and nanowire structures, is of great interest to the nano-optics community. Nanowires and nanoslots confine electromagnetic energy by supporting counter propagating surface plasmon polariton (SPP) waves which, through interference, setup Fabry−Perot type resonances . Recent advances in the technology of new generation electron microscopes has yielded exciting new experimental and theoretical studies on the behavior of Fabry−Perot type surface plasmon resonances in nanowires [12–17]. In addition, surface plasmon resonances setup in nanoholes and slots in free standing thin silver films have been studied in the transmission electron microscope (TEM) [18,19]. Recently, plasmonic maps from complimentary split-ring resonator structures of different sizes have been acquired in the TEM, demonstrating Babinet’s principle at the nanoscale . However, a direct comparison of the plasmonic response of complementary systems of the same size has not been undertaken. Given the importance of nanofabrication methods in engineering nanostructures with tailored optical properties, it is important to explore whether complementary structures of nanoscale dimensions obey known bulk physical phenomena, such that the easiest and most effective route of fabrication (either bottom up or top down) can be used.
Plasmon oscillations in metallic structures are excited in the TEM impulsively by the transient field of the fast electron . By performing electron energy loss spectroscopy (EELS) in a TEM equipped with a monochromator and an energy filtering spectrometer, we can measure small changes in the kinetic energy of the incident electron beam after having passed through a thin specimen. The excitation of plasma oscillations in silver occur at energy losses below a few eV, corresponding to the near infrared to ultraviolet region of the electromagnetic spectrum, requiring the use of a high-resolution EELS spectrometer and electron monochromator to resolve their distribution. Using a modern TEM with sub-eV energy resolution we resolve multipolar plasmonic excitations in a silver nanowire and nanoslot.
In our experiment, we simultaneously collect high and low angle electron scattering intensity from with a focused electron probe scanning the nanometallic objects in the TEM. During data acquisition, the electron probe, a few nanometers in diameter, is scanned in a raster over a defined rectangular region. At each position in the raster, both high angle scattered electrons are collected with an annular dark field (ADF) detector, and low angle scattered electrons, which enter a magnetic energy-loss spectrometer, are recorded as electron energy loss spectra (Fig. 1 insert). The resulting data set comprises a 2D image of the object from the ADF detector (Fig. 2A,B ), and a 3D spectrum image from the spectrometer, both sharing the same x,y position coordinates of the probe scan. In this configuration, individual spectra can be selected and analyzed from any position in the 2D scan with nanometer precision. Details on the fabrication of the nanowire and nanoslot are provided in the supplementary information section.
3. Results and discussion
Figure 1 displays the recorded electron energy signals from a silver nanowire and nanoslot of comparable dimensions, (754 x 56) nm and (760 x 61) nm respectively. Both spectra have had the zero loss tail removed by reflected tail subtraction, and they are vertically aligned to each other by the signal above 4 eV. Remarkably, both structures exhibit multiple peaks in their spectra at similar energy losses, ranging from 0.42 eV to 1.99 eV, and at 3.5 eV. The peaks in the spectra are due to the transfer of small fractions of kinetic energy from the fast electron to the excitation of electron plasma oscillations in the nanowire and nanoslot. At 3.47 eV, an electrostatic transverse oscillating surface plasmon is excited, due to the curvature of the cylinder, in agreement with the surface plasmon resonance energy of spherical silver nanoparticles. The series of peaks below 2 eV belong to propagating longitudinal SPP excitations.
Figure 2 displays the spatial origin of inelastic electron scattering events at energy transfers belonging to peak positions in the EELS signal. The intensity variation in the series of energy filtered spatial maps is representative of the electron energy loss probability, given by the photonic local density of states (LDOS) . The maps from both the nanoslot and nanowire display a simple standing wave pattern in the LDOS, setup by the interference of counter propagating SPPs. This interference results in the creation of nodes and antinodes in the LDOS over the length of the supporting structure, creating standing wave harmonics of increasing energy. Interestingly, the position of the nodes and antinodes in the nanoslot and nanowire are reversed for a given resonant mode. This inversion of phase is consistent with Babinet’s principle, which predicts that the sum of the radiation pattern from complementary structures is equal to the radiation pattern with no structures present. Alternatively, the radiation patterns from the nanoslot and nanowire are opposite in phase and equal in magnitude.
Under closer inspection, more subtle differences in the plasmonic response of the nanoslot and nanowire are apparent. Figure 3 compares the line profiles of the resonance modes setup in both structures. The resonance profiles from the nanoslot have a uniform antinode height and separation across the length of the slot, and end minima closely coincide with the ends of the nanoslot geometry. Conversely, the antinode amplitude is significantly damped at the terminals of the nanowire. We attribute terminal damping to the radiative decay of the SPP at the sharply curved terminals, thereby reducing the energy of the reflected SPP wave. Furthermore, the end maxima do not closely coincide with the end nanowire terminals, particularly on the right hand side. We attribute this shift to the presence of a thick region on the TEM carbon support grid, whose influence is visible in the energy-filtered image in Fig. 2.
In summary, we have demonstrated Babinet’s principle in two complementary structures of comparable size; a silver nanowire and a nanoslot in a silver film, by measuring the energy loss of a scanning electron beam. Both structures support counter-propagating surface plasmon polaritons, which through interference setup multiple resonance harmonics. The recorded resonance energies of the nanoslot and nanowire closely coincide, however, the harmonic plasmonic fields are opposite in phase, in agreement with Babinet’s principle. Therefore, when designing nanostructures to exhibit desired optical properties, effective use of this principle can be applied even at the nanoscale, providing an alternative route of fabrication, bottom up or top down as the case may be.
Appendix A: Supplementary information
The silver nanowire sample was prepared by depositing and drying a few microliters of single crystal silver nanowire aqueous solution, (NanoComposix) onto an ultrathin 3 mm carbon grid (Ted Pella). Thin areas of the carbon support were less than 3 nm thick. The silver nanoslot was milled into a 200 nm thick silver film, supported on an ultrathin carbon grid, by a focused ion beam. EELS data were acquired on an ultrastable FEI Titan TEM operated at 80 kV at the Canadian Centre for Electron Microscopy. The TEM is equipped with an electron monochromator, a spherical aberration corrector of the image-forming lens and a Gatan Tridiem spectrometer. EELS data were recorded at 0.09 eV (average FWHM) energy resolution. Electron energy loss spectra were recorded with a post column prism fitted with a two-dimensional charge-coupled device camera (256 x 2048 pixels) at an energy dispersion of 0.01 eV per pixel. To speed up data readout, a vertical binning of 16 was used with an exposure time of 2 ms per pixel. All EELS datasets were aligned by Gaussian fitting of the zero loss peaks, and the zero loss peaks were subsequently removed by the reflected tail subtraction method. A mask was applied to each energy filtered image in Fig. 2 in place of the silver nanowire and silver film, where strong electron scattering significantly reduced the signal quality from these areas. The EELS data were not de-convoluted. The energy-filtered maps displayed in Fig. 2 were integrated over an energy window of 0.20 eV.
The experimental work presented here was carried out at the Canadian Centre for Electron Microscopy (CCEM), a national facility supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and McMaster University. GAB is grateful to NSERC for a Discovery Grant for supporting this work.
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