Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> A simple theory of electronic and ionic oscillations in an ionized gas has been developed. The electronic oscillations are so rapid (ca. ${10}^{9}$ cycles) that the heavier positive ions are unaffected. They have a natural frequency ${\ensuremath{\nu}}_{e}={(\frac{n{e}^{2}}{\ensuremath{\pi}m})}^{\frac{1}{2}}$ and, except for secondary factors, do not transmit energy. The ionic oscillations are so slow that the electron density has its equilibrium value at all times. They vary in type according to their wave-length. The oscillations of shorter wave-length are similar to the electron vibrations, approaching the natural frequency ${\ensuremath{\nu}}_{p}={\ensuremath{\nu}}_{e}{(\frac{{m}_{e}}{{m}_{p}})}^{\frac{1}{2}}$ as upper limit. The oscillations of longer wave-length are similar to sound waves, the velocity approaching the value $v={(\frac{k{T}_{e}}{{m}_{p}})}^{\frac{1}{2}}$. The transition occurs roughly (i.e. to 5% of limiting values) within a 10-fold wave-length range centering around $2{(2)}^{\frac{1}{2}}\ensuremath{\pi}{\ensuremath{\lambda}}_{D}$, ${\ensuremath{\lambda}}_{D}$ being the "Debye distance." While the theory offers no explanation of the cause of the observed oscillations, the frequency range of the most rapid oscillations, namely from 300 to 1000 megacycles agrees with that predicted for the oscillations of the ultimate electrons. Another observed frequency of 50 to 60 megacycles may correspond to oscillations of the beam electrons. Frequencies from 1.5 megacycles down can be attributed to positive ion oscillations. The correlation between theory and observed oscillations is to be considered tentative until simpler experimental conditions can be attained. <s> BIB001 </s> Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> The behavior of the electrons in a dense electron gas is analyzed in terms of their density fluctuations. These density fluctuations may be split into two components. One component is associated with the organized oscillation of the system as a whole, the so-called "plasma" oscillation. The other is associated with the random thermal motion of the individual electrons and shows no collective behavior. It represents a collection of individual electrons surrounded by comoving clouds of charge which screen the electron fields within a distance of the order of magnitude of the Debye length. This split up of the density fluctuations corresponds to an effective separation of the Coulomb interaction into long-range and short-range parts; the separation occurs at roughly the Debye length. <s> BIB002 </s> Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> The behavior of the electrons in a dense electron gas is analyzed quantum-mechanically by a series of canonical transformations. The usual Hamiltonian corresponding to a system of individual electrons with Coulomb interactions is first re-expressed in such a way that the long-range part of the Coulomb interactions between the electrons is described in terms of collective fields, representing organized "plasma" oscillation of the system as a whole. The Hamiltonian then describes these collective fields plus a set of individual electrons which interact with the collective fields and with one another via short-range screened Coulomb interactions. There is, in addition, a set of subsidiary conditions on the system wave function which relate the field and particle variables. The field-particle interaction is eliminated to a high degree of approximation by a further canonical transformation to a new representation in which the Hamiltonian describes independent collective fields, with ${n}^{\ensuremath{'}}$ degrees of freedom, plus the system of electrons interacting via screened Coulomb forces with a range of the order of the inter electronic distance. The new subsidiary conditions act only on the electronic wave functions; they strongly inhibit long wavelength electronic density fluctuations and act to reduce the number of individual electronic degrees of freedom by ${n}^{\ensuremath{'}}$. The general properties of this system are discussed, and the methods and results obtained are related to the classical density fluctuation approach and Tomonaga's one-dimensional treatment of the degenerate Fermi gas. <s> BIB003 </s> Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> The effects of the Coulomb interaction between free electrons in an electron gas are considered for a variety of phenomena. The analysis is based on the collective description, which describes the long-range correlations in electronic positions (due to the Coulomb force) in terms of the collective oscillations of the system as a whole. It is shown that an independent electron model should provide a good description of the electrons in a metal in many cases of interest. The ground state energy of the free electron gas is determined, and an estimate of the correlation energy is obtained, with results in good agreement with those of Wigner. The exchange energy is shown to be greatly reduced by the long-range correlations, so that its effect on the level density and the specific heat is comparatively slight, leading to an electronic specific heat for Na which is approximately 80 percent of the free-electron value. The possible ferromagnetism of a free-electron gas is investigated, and it is found that the long-range Coulomb correlations are such that a free-electron gas will never become ferromagnetic (no matter how low the density). The excitation of the collective oscillations by a fast charged particle is studied, and the semiclassical results obtained by Bohm and Pines are verified by a quantum-mechanical calculation. The results are applied to the experiments of Ruthermann and Lang on the scattering of electrons by thin metallic films and to experiments on the stopping power of light metals for fast charged particles, with resulting good agreement between theory and experiment. <s> BIB004 </s> Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> Since the introduction of optical fiber technology in the field of sensor based on the technique of surface plasmon resonance (SPR), fiber-optic SPR sensors have witnessed a lot of advancements. This paper reports on the past, present, and future scope of fiber-optic SPR sensors in the field of sensing of different chemical, physical, and biochemical parameters. A detailed mechanism of the SPR technique for sensing purposes has been discussed. Different new techniques and models in this area that have been introduced are discussed in quite a detail. We have tried to put the different advancements in the order of their chronological evolution. The content of the review article may be of great importance for the research community who are to take the field of fiber-optic SPR sensors as its research endeavors. <s> BIB005 </s> Carbon-Based Nanomaterials for Plasmonic Sensors: A Review <s> Plasmonics <s> Surface plasmon resonance technique in collaboration with optical fiber technology has brought tremendous advancements in sensing of various physical, chemical, and biochemical parameters. In this review article, we present the principle of SPR technique for sensing and various designs of the fiber optic SPR probe reported for the enhancement of the sensitivity of the sensor. In addition, we present few examples of the surface plasmon resonance- (SPR-) based fiber optic sensors. The present review may provide researchers valuable information regarding fiber optic SPR sensors and encourage them to take this area for further research and development. <s> BIB006
It is known that the phenomenon of oscillations plays a crucial role in the universe and is found in almost every object. The oscillations of electrons are responsible for all the interesting phenomenon in electromagnetic theory. In the 19th century, Maxwell theoretically predicted the existence of electromagnetic (EM) waves, which was later experimentally demonstrated by Hertz. In 1902, Woods reported the uneven distribution of light in a diffraction grating spectrum, known as Wood's anomalies  . In 1928, Langmuir studied oscillations in ionized gas BIB001 . Later, Pines and Bohm stated that the energy losses experienced by fast electrons in passing through foils are due to the excitation of plasmons with the resonance frequency in bulk plasma, as  BIB002 BIB003 BIB004 : where n, e, and m are the density, charge, and mass of the electron, respectively, while ε0 is the permittivity of the vacuum. In 1957, Ritchie found that anomalous energy loss occurs in a metal thin film  . Later, Stern and Ferrell studied plasma oscillations and for the first time, in 1960, introduced the name surface plasmons  . Thus, surface plasmons are the coherent oscillations of charges at the surface of plasmonic materials. After a lot of research, it was found that the plasmons can be excited by various quantized energies, such as photons, phonons, and electrons. The coupling between the surface plasmons and photons is named surface plasmon polaritons. The solution of Maxwell's equations for a metal/dielectric interface under appropriate boundary conditions gives the following dispersion relationship of surface plasmons BIB005 BIB006  : where εm and εd are the dielectric constants of metal and dielectric and k0 is the wave vector of light in free space. Figure 1 shows the dispersion plots of surface plasmons and direct light. It may be noted from these plots that the surface plasmons dispersion curve never intersects the dispersion curve of direct light. This implies that no phase matching or momentum matching is possible between these two wave vectors and, therefore, the surface plasmons cannot be excited by direct light. For the excitation of surface plasmons an extra momentum is required. This can be achieved by using some special structures, like prism or grating. In 1968, Otto gave a prism-based configuration where the excitation of the surface plasmons was achieved by means of an evanescent wave. In this configuration, a high index prism is kept near a metal surface, as shown in Figure 2a . The air gap between the prism base and metal surface is maintained in nanometer range. When the light incident on the base of the prism is at an angle higher than the critical angle, the total internal reflection takes place and an evanescent wave is generated at the interface of prism and air. The evanescent wave excites the surface plasmons at the interface of air and metal. In Figure 1 , it can be seen that the dispersion curve of the evanescent wave intersects the dispersion curve of the surface plasmons and, at the point of intersection, the wave vector of the evanescent wave matches with the wave vector of the surface plasmon wave, resulting in the excitation of the surface plasmons. This is called surface plasmon resonance. The resonance occurs at a particular angle, called the resonance angle. At the resonance angle the reflected light intensity shows a minimum value. The maintenance of the finite gap between the base of the prism and metal layer requires a sophisticated and bulky setup. To avoid this, Kretschman and Reather modified the Otto configuration. In this configuration, a thin metal film is coated over the base of the prism and placed in contact with the dielectric medium, as shown in Figure 2b [21] . In 1968, Otto gave a prism-based configuration where the excitation of the surface plasmons was achieved by means of an evanescent wave. In this configuration, a high index prism is kept near a metal surface, as shown in Figure 2a . The air gap between the prism base and metal surface is maintained in nanometer range. When the light incident on the base of the prism is at an angle higher than the critical angle, the total internal reflection takes place and an evanescent wave is generated at the interface of prism and air. The evanescent wave excites the surface plasmons at the interface of air and metal. In Figure 1 , it can be seen that the dispersion curve of the evanescent wave intersects the dispersion curve of the surface plasmons and, at the point of intersection, the wave vector of the evanescent wave matches with the wave vector of the surface plasmon wave, resulting in the excitation of the surface plasmons. This is called surface plasmon resonance. The resonance occurs at a particular angle, called the resonance angle. At the resonance angle the reflected light intensity shows a minimum value. The maintenance of the finite gap between the base of the prism and metal layer requires a sophisticated and bulky setup. To avoid this, Kretschman and Reather modified the Otto configuration. In this configuration, a thin metal film is coated over the base of the prism and placed in contact with the dielectric medium, as shown in Figure 2b [21] . The resonance condition of surface plasmons is highly susceptible to change in the dielectric constant of the medium adjacent to the metal layer. This fact has been extensively utilised for the design of highly sensitive plasmonic sensors. They are broadly classified as propagating surface plasmon resonance (SPR) sensors or localized SPR sensors, depending on the utilization of thin film or nanomaterials of metals BIB005 BIB006 .