Fano Resonance in Nanostructures by QED

PITTSBURGH - May 7, 2015 - PRLog -- .

Introduction
Absorption spectra of gases usually show a symmetric shape about resonance lines. In 1935, Beutler [1] observed the spectral absorption of some lines of the noble gases showed sharp asymmetric shapes. Fano [2] proposed the asymmetry was caused by the QM superposition principle. QM stands for quantum mechanics. Fano suggested the Beutler spectra showing the unusual asymmetry was the consequence of an interference phenomenon between alternative mechanisms of excitation.

The Fano resonance may be understood with the simple spring-mass system shown in the thumbnail. System 1 corresponds the surrounding gas atoms. System 2 represents an individual atom coupled to System 1 by a spring. System 1 is driven by the excitation source. System 2 is indirectly excited by the spring. The System 1 response produces a symmetric shape, but includes the effect of the individual atom reflected as an asymmetric shape, the latter called the Fano resonance. The System 2 response of the individual atom produces only symmetric shapes.

In the Fano resonance observed by Beutler in the absorption spectra of gases, the interference is caused [3] by the difference between direct ionization and auto-ionization, say by the photo-ionization of atom A by the quantum hv. Direct ionization occurs in System 1, i.e., A + hv → A⁺ + e producing the charged atom A⁺ and electron e. Auto-ionization differs by producing quasi-bound excited states A* that subsequently ionize, i.e., A*→ A⁺ + e. In effect, Fano resonance may therefore be considered as the QM interference between direct ionization and auto-ionization as Fano first proposed.

Fano resonance in NS containing a number of atoms is analogous [4] to the interference between the response of an individual gas atom with the atoms of the surrounding gas. NS stands for nanostructures.

Problems
One problem is the analogy of Fano resonance in gas atoms to NS is the source of auto-ionization of NS atoms excited only by IR excitation. UV light would auto-ionize the NS atoms, but is not used. Fano resonance in NS atoms based on plasmons is therefore questionable because the NS atoms are required to undergo auto-ionization which is not possible with IR excitation. Simply put, NS excitation sources using IR light are incapable of auto-ionizing the NS atoms as required for Fano resonance. Yet, Fano resonance experiments have been conducted with IR light to explain a multitude of NS observations in the literature even though the condition of auto-ionization of NS atoms required for the validity of the Fano resonance is not justified.

Another problem is how does auto-ionization of NS atoms proceed, as it somehow does, if only IR radiation is used in Fano experiments. For example, the application of surface plasmons to the dynamics of a circular disk inside a ring produces a response of symmetric and asymmetric plasmons that are thought [5] to combine to produce the asymmetric Fano resonance. However, how the IR light causes the auto-ionization required to produce the Fano resonance is not described. Indeed, plasmons cannot combine to produce Fano resonances unless the IR excitation somehow creates the auto-ionized states of the disk and ring atoms. What this means is NS somehow frequency up-convert IR excitation to the UV levels necessary for auto-ionization in order for the Fano resonances to be observed. Moreover, surface plasmons lack a mechanism for frequency up-conversion of EM radiation from the IR to levels beyond the UV suggesting that only a photon based theory based on QED explains the observed Fano resonance reported in the literature. EM stands for electromagnetic and QED for quantum electrodynamics.

Proposal
Consistent with the Fano resonance based on auto-ionization, QED induced EM radiation beyond the UV is indeed produced from IR light in NS. QED is based on the QM interpretation of the atom as a harmonic oscillator that precludes the atoms at the nanoscale from having the heat capacity to conserve absorbed EM energy by an increase in temperature. Instead, the EM energy is conserved by frequency up-conversion to the TIR resonance of the NS. TIR stands for total internal reflection. See numerous QED applications at http://www.nanoqed.org/, 2010 – 2015.

Theory
QED induced EM radiation is confined almost totally in the TIR mode of the NS because of their high surface to volume ratio. The EM radiation created in the NS has TIR wavelength λ at frequency υ = (c/n)/λ, where c is the velocity of light and n the refractive index of the NS. The TIR wavelength λ depends on the NS geometry, but may be bracketed between 2d (for thin films) and πd (for a spherical particle), where d is the dimension between NS surfaces. QED radiation is therefore created in the NS surface having Planck energy E = hυ. Since NS have nanometer dimensions, the Planck energy E is more than sufficient to auto-ionize the atoms necessary in the theory of Fano resonance

Discussion
Photo-excitation of surface plasmons in 85 nm Ag nanowires excited by Ti-sapphire IR laser at 800 nm is thought [6] to produce highly localized melting. However, QM precludes temperature increases and melting in nanowires. Numerical plasmon solutions by Maxwell’s equations showing melting exclude QM are therefore simply not valid. Instead, the QED radiation ionizes the nanowire leaving a highly charged state of atoms that undergo Coulomb explosion to produce the fragmentation of submicron particles observed. Ibid.

Conclusions
The Fano resonance is the consequence of QM that precludes the atom from having the heat capacity to conserve EM energy by an increase in temperature. Instead, conservation proceeds by the QED induced frequency up-conversion of IR radiation beyond the UV to auto-ionize the NS atoms - a necessary condition to observe the Fano resonance.

With the NS atoms auto-ionized, the NS responds to IR excitation in a symmetric absorption shape, but interference from quasi-bound states of individual atoms created by auto-ionization produces the superposed asymmetric Fano resonance shape.

Surface plasmon solutions by Maxwell’s equation are not valid by QM and need to be corrected.

References
[1] H. Beutler, “Über absorptionsserien von argon, krypton und xenon,” Z. Phys. A 93, 177–196, 1935.
[2] U. Fano, “Sullo spettro di assorbimento dei gas nobilipresso il limite dello spettro d’arco,” Nuovo Cimento,12, 154–161, 1935.
[3] A. E. Miroshnichenko, et al., "Fano resonances in nanoscale structures," Rev. Mod. Phys., 82, 2261 - 2298, 2010
[4] B. Luk’yanchuk, et al., the Fano resonance in plasmonic nanostructures and metamaterials,” Nature Mat., 9, 707-715, 2010.
[5] F. Hao, et Al., “Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B, 76, 245417, 2007.
[6] L. Liu, et al., “Highly localized heat generation by femtosecond laser induced plasmon excitation in Ag nanowires,” Appl. Phys. Lett., 102, 073107, 2013.