In this chapter, we discuss electromagnetic description of metal gap structures in three distinct regimes of the gap width: (1) sub-sheet depth, (2) min- to sub-nanometer, and (3). At the lowest order gap plasmon mode, x-components of the electric fields in the gap and the metal have the form Here β is the propagation constant of the gap plasmon mode, with the gap width, and kgap (kmetal) denotes wave vector component perpendicular to the interface in the gap (metal).
The broadening does not depend on the gap width and is affected only by the Fermi velocity of the electrons. This is likely to change the optical properties of the gap dramatically, but in some cases not that much. We now attempt to establish a relationship between these R–C parameters and the effective optical transmission of the slit.
Out-of-plane-oriented point gaps: tip- based approach
Once the dielectric is completely etched and the void is filled with water molecules, the hot spot can be filled with other materials, including alcohols and dye molecules through diffusion and dilution. Complete etching of the gap-filling dielectric can be confirmed by energy-dispersive X-ray spectroscopy (EDS) mapping of the cross-sectional transmission electron microscope (TEM) image and by spectral shifts in terahertz transmission after etching and gap filling . By using the critical point dryer (CPD) to remove the gap-filling water after wetting, catastrophic gap collapse due to surface tension can be prevented and void gaps as wide as 1.5 nm can be achieved [120].
It should also be noted that the gap thus produced can be further narrowed by a factor of ~2 using thermal expansion of metals when the gap width is an order of magnitude smaller than the periodicity or the overall size of the metal layer [108]. Gap distances are controlled by feedback mechanisms typical of atomic force microscopy (AFM) and scanning tunneling microscopy (STM). STM facilitates a tunneling current between the conductive probe and the substrate, which is strongly affected by the distance between them, allowing control of the gap width in tens.
The magnitude of the cantilever deflection can be converted to the atomic force between the tip tip and the sample surface, which can be facilitated for controlling the gap distance response of the AFM in a range of several nanometers. In addition, AFM can be applied to samples with height differences of several micrometers, which is much larger than those in STM. Feedback control using the shear force between the side-oscillating probe and the sample surface can be implemented by attaching the sharp metal probe to corroded piezo components such as quartz tuning forks.
Shear force-feedback controlled slit can be operated at room temperature and atmospheric pressure, and slit spacing of 2-3 nm can be maintained. It should also be noted that the tip-based gap can also be applied at infrared and terahertz frequencies, and pump-probe-type experiments are also performed to map ultrafast nanoscale dynamics.
In-plane-oriented point-gaps
Equipped with chemically etched metal tip probe, also used in STM, shear force feedback controlled gap enabled highly efficient light-matter interaction. Recently, local excitation of excitons in 2D material at the adjacent area between sharp Au metal probe and snare shape nanostructure was demonstrated using shear force feedback controlled gap [ 31 ]. It should also be noted that the point-based gap can also be applied to infrared and terahertz frequencies and pump-probe type experiments are also performed for nanoscale mapping of ultrafast dynamics [ 147 , 148 ].
The formation of the junction can be observed in real time by monitoring the jump in resistance across the wire. The metal wire is placed on top of a flexible substrate, which is usually attached at both ends. The ultrapure metallic contacts are very useful for making molecular compounds, but can also be used for optical applications.
The antenna also supports localized surface plasmon resonances in the near-infrared, such that 785 nm irradiation leads to a strong enhancement of the electromagnetic field at the gap and, consequently, photon-induced tunneling. Although generally considered a defect in an electronic circuit, electromigration can be used to produce gaps of a few to one nanometer on a very large scale. Giant field enhancement in the gap can expand the structure by plasmonic heating, which enables switching of metallic point contacts by controlling light intensity or polarization [170].
The tunnel junction can also be used as an efficient source of electroluminescence, as the local density of optical states is greatly enhanced in the subnanometer plasmonic gap [171]. Because of the extreme confinement of the electromagnetic field and the gain in the gap, the authors were able to perform terahertz spectroscopy on a single fullerene molecule placed in a gap approximately 400,000 times smaller than the wavelength.
In-plane-oriented extended gaps
As the method is based on atomic layer lithography, the 'healable gap' can be fabricated at wafer scale with essentially no limitation in the overall size of the gap (Figure 17). After bending the entire sample, slits narrowed from 20 nanometers to zero and became optically equivalent to a bare metal film. The method shows high switching contrast especially at terahertz and microwave frequencies because only partial contact between the two metal layers forming the gap can completely screen the gap, as shown in Section 1.3.
Therefore, the method is essentially to embed prepatterned cracks in a lithographically controlled manner, which the authors call their sample 'zerogap'. The strength of this approach is that the 'off state' – a state without applied load – corresponds to the minimum gap width, so that the structure is robust against fatigue or other sources of degradation. The slot array fabricated by the authors shows an on-off ratio of 105 with 'on-state' transmission greater than 85% and shows no fatigue after 10,000 times of switching. In this work, photoresist is first patterned on a thin metal film deposited on top of a polydimethylsiloxane/polyimide (PDMS/PI) substrate.
By removing the resist, an array of closely packed (200 cm−1), 5 mm long metal slits is created. It should be noted that such substrate adaptation is not limited to flexible elastomers; electromechanical modulation of semiconductor thin films can also be used to tune the gap width and plasmonic dimer by decoupling. In previous chapters, we reviewed the electromagnetic description of gaps below 10 to zero nanometers and the various ways to create them.
While the holes themselves are already useful as photonic elements, integrating the hole with various semiconductors, molecules and quantum materials could also reveal pathways to many unexplored phenomena. In the following sections, we will give an overview of applications of nano- and zero-nanometer gaps.
Strong coupling of light and matter
When the rate of energy exchange between material and photonic resonances is greater than any other rate of energy loss in the system, the two resonances are said to be strongly coupled. In this regime, material and photonic modes hybridize and form polaritons and exhibit characteristic anti-crossing behavior known as Rabi splitting [194]. Such strongly coupled systems can involve many interesting quantum phenomena, including the ultra-low-threshold lasing of the Bose-Einstein condensate and single-photon nonlinearity, etc.
The coupling strength is determined by the transition dipole moment of the resonant material, local field enhancement introduced by the photonic mode and their spatial overlap. It is worth mentioning that it is possible to increase the transition dipole moment by means of collective coupling [205–207] . Nevertheless, in this section we focus on strong coupling phenomena observed in nanoplasmonic systems, which can seamlessly integrate with various nanometer-sized and low-dimensional materials (Figure 18).
Here the bright mode of the plasmonic resonance couples strongly to excitonic resonance and exhibits a Rabi splitting of 230 meV, which is 12% of the resonant frequency. The large Rabi splitting is attributed to a large transition dipole moment of the well-aligned J-aggregate complex. G Strong coupling of dye molecules to the gap plasmon mode, which only occurs when the transition dipole moment of the dye molecules aligns with the enhanced electric field at the gap.
When the number of layers reaches seven or more, an out-of-plane component of the exciton arises due to multilayer-induced mixing, and strong coupling with a Rabi splitting of 140 meV is observed. The importance of alignment between the increased electric field and the transient dipole moment is also emphasized in the research of Chikkaraddy et al., where the authors observe strong coupling in a 0.9 nm thick film of methylene blue dye only when the transient dipole moment is aligned parallel to the increased electric field in gaps [212].
Photochemistry
Full control of long wavelength radiations for 5/6G communications
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