Plasmon Wavefunctions

Spatial resolution. In optics, to realize the ultimate resolution like that of STM, several breakthroughs may still be needed. However, wavefiinctions of elementary excitations such as excitons and plasmons can be visualized if a sufficiently high spatial resolution is achieved. Near-field optical microscopy is promising for this purpose. Wide special range and compatibility with dynamic measurements are the great advantages of optical methods and allow one to study materials properties from broad points of view. Here, the principles of visualization of wavefimctions using a near-field optical microscope will be briefly described in comparison with that of STM. 

STM detects elecflic currents due to tunnel electrons between the sample and the probe tip. Tunneling probability at the tip position is dependent on the overlap of electronic wavefiinctions between the sample and the tip. Because the wavefunction of the electron at the tip is localized on a single atom, STM visualizes the electronic local density-of-states (LDOS) of the sample at tip position T and energy E with atomic resolution [50,51]. Operation principles of a near-field optical microscope is similar to that of an STM [52,53]. Instead of using tunnel electrons as in an STM, a near-field optical microscope uses tunnel photons between the sample and the near-field probe tip and visualizes photonic LDOS at position V and frequency co. In general, LDOS is defined by the following equation [54]. 

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The spatial feature is in excellent agreement with the calculated photonic LDOS at the excitation wavelength. The spatial feature of the image is assigned to the plasmon wavefunction of w = 2 mode. Similarly, a near-tield transmission image taken at 900 nm (Fig. 4.1 Id) is assigned the plasmon wavefunction of w = 1 mode. To examine the ultrafast dynamics in the nanorod, the one-color EPC method was adopted, with near-infrared pulses as the excitation sources. At the excitation wavelength, both the w = 1 and m = 2 modes were excited at the same time. In EPC, the... 

In the near future, dynamic visualization of plasmon wavefunctions will become more important. Experimentally, however, imaging with time resolutions shorter than the lifetime of a plasmon (<20 fs) is a challenge. On the other hand, electromagnetic field calculation has fewer barriers and is feasible. Calculation protocols with high precision, high reliability, and reasonable computational cost are expected to be developed and applied to reveal the dynamic features of plasmon wavefunctions. 

H. Okamoto and K. Imura, Near-field imaging of optical field and plasmon wavefunctions in metal nanoparticles. Journal of Materials Chemistry, 16(40), 3920-3928 (2006). 

Wavefunction Images of Plasmon Modes of Cold Nanorod — Near-Field Transmission Method... 

In summary, it has been demonstrated that plasmon-mode wavefunctions of gold nanoparticles resonant with the incident light can be visualized by near-field transmission imaging. 

In this chapter, we have provided an overview of near-field imaging and spectroscopy of noble metal nanoparticles and assemblies. We have shown that plasmon-mode wavefunctions and enhanced optical fields of nanoparticle systems can be visualized. The basic knowledge about localized electric fields induced by the plasmons may lead to new innovative research areas beyond the conventional scope of materials. 

Near-Field Optical Imaging of Wavefunctions and Optical Fields in Plasmonic Nanostructures... 

Abstract Plasmonic nanostructures exhibit unique optical properties, and fundamental studies of these structures are relevant to wide range of research areas, both fundamental and applied. Potential applications of the plasmonic nanostructures originate from their ability to confine (and sometimes propagate as well) optical fields in nanometer scales, and are closely related to the static and dynamic properties of plasmonic waves. In this chapter, visualization of wavefunctions and optical fields in plasmonic nanostructures using near-field linear and non-linear optical methods is described. 

Plasmon modes with odd parity characters are dipolar forbidden because no polarization is created upon photo-excitation. Observation of the odd plasmon mode in Fig.4.7d indicates that the optically forbidden mode becomes optically allowed by the local illumination of the near-fleld. It is also noted that observation of the wavefunction image indicates that the coherence of the polarization wave extends from the tip position to the whole area of the nanorod. 

Basic studies on plasmons and their related materials will influence wider research areas in fundamental and applied fields. Among them, applications of plasmonic optical fields to photochemical reactions have a large impact in photo-and material-sciences. For instance, the interaction between localized optical (or plasmon) fields with molecular electronic wavefunctions may enhance photochemical reaction rates, which is sometimes forbidden under the far-field irradiation of light. It has a potential to open up new chemical reaction routes beyond the dipolar approximation. Such novel photochemical reactions shed new light on photo- and material-sciences. 

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