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Minimal spaser threshold within electrodynamic framework: Shape, size and modes.

Arnold N, Hrelescu C, Klar TA - Ann Phys (2015)

Bottom Line: Here, we derive this result from the purely classical electromagnetic scattering framework.Furthermore, retardation is included straightforwardly into our framework; and the global spectral gain minimum persists beyond the quasi-static limit.We illustrate this with two examples of widely used geometries: Silver spheroids and spherical shells embedded in and filled with gain materials.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied PhysicsJohannes Kepler University LinzAltenbergerstraße 694040 LinzAustria; Soft Matter PhysicsJohannes Kepler University LinzAltenbergerstraße 694040 LinzAustria.

ABSTRACT

It is known (yet often ignored) from quantum mechanical or energetic considerations, that the threshold gain of the quasi-static spaser depends only on the dielectric functions of the metal and the gain material. Here, we derive this result from the purely classical electromagnetic scattering framework. This is of great importance, because electrodynamic modelling is far simpler than quantum mechanical one. The influence of the material dispersion and spaser geometry are clearly separated; the latter influences the threshold gain only indirectly, defining the resonant wavelength. We show that the threshold gain has a minimum as a function of wavelength. A variation of nanoparticle shape, composition, or spasing mode may shift the plasmonic resonance to this optimal wavelength, but it cannot overcome the material-imposed minimal gain. Furthermore, retardation is included straightforwardly into our framework; and the global spectral gain minimum persists beyond the quasi-static limit. We illustrate this with two examples of widely used geometries: Silver spheroids and spherical shells embedded in and filled with gain materials.

No MeSH data available.


Multipolar thresholds for metallic shells. The inset shows the geometry of the GMG structure. A metallic shell with the dielectric function ε2 = εAg from Johnson and Christy is immersed into and filled with a gain medium with ε3 = ε1 = 2.6+iε1″. The threshold gain values −ε1″ = −εthr″ (left column, log‐color map) and the wavelengths λthr (right) are shown as contour plots as a function of the inner radius a1 and the shell thickness h2. Different plots correspond to different multipolar modes from l = 1 (dipole), to l = 5, as labeled in the panels.
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andp201500318-fig-0003: Multipolar thresholds for metallic shells. The inset shows the geometry of the GMG structure. A metallic shell with the dielectric function ε2 = εAg from Johnson and Christy is immersed into and filled with a gain medium with ε3 = ε1 = 2.6+iε1″. The threshold gain values −ε1″ = −εthr″ (left column, log‐color map) and the wavelengths λthr (right) are shown as contour plots as a function of the inner radius a1 and the shell thickness h2. Different plots correspond to different multipolar modes from l = 1 (dipole), to l = 5, as labeled in the panels.

Mentions: The quasi‐static expression (7) shows that for a solid spherical metal particle in a gain medium the dipole mode l=1 is the easiest to generate, as it requires the lowest gain ɛG′′=−ɛM′′/2, while higher multipole thresholds approach the limit ɛG′′=−ɛM′′. For the active void (eq. (8)) the situation is reversed. The dipolar mode requires the largest gainɛG′′=−2ɛM′′, while higher multipoles approach the limit ɛG′′=−ɛM′′. Metallic nano‐shells which have gain both inside and outside (see sketch in the upper right hand corner of Fig. 3), possess both sphere‐ and void‐like features, which makes their ordering of thresholds worth to investigate. For the most of the remaining section, we focus on the symmetric structures, with the same gain material inside and outside a silver shell of radius a1 and thickness h2. A comparison with asymmetric gain distributions, where the gain is either only in the core, or only outside the shell will be given at the end of this section. We will call the symmetric geometry GMG (gain/metal/gain), the case of a gain filled shell with passive dielectric ε3 outside GMε3, and the case of a metallic shell on a gainless core, but with gain outside a ε1MG structure. Asymmetric structures have been discussed before 5, 57, but largely for the quasi‐static dipole case and without global gain optimization via geometry. We note that in the main text, we use full analytical multi‐shell Mie theory without approximations. Quasi‐static approximations can be found in Supp. Info. 6.


Minimal spaser threshold within electrodynamic framework: Shape, size and modes.

Arnold N, Hrelescu C, Klar TA - Ann Phys (2015)

Multipolar thresholds for metallic shells. The inset shows the geometry of the GMG structure. A metallic shell with the dielectric function ε2 = εAg from Johnson and Christy is immersed into and filled with a gain medium with ε3 = ε1 = 2.6+iε1″. The threshold gain values −ε1″ = −εthr″ (left column, log‐color map) and the wavelengths λthr (right) are shown as contour plots as a function of the inner radius a1 and the shell thickness h2. Different plots correspond to different multipolar modes from l = 1 (dipole), to l = 5, as labeled in the panels.
© Copyright Policy - creativeCommonsBy
Related In: Results  -  Collection

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andp201500318-fig-0003: Multipolar thresholds for metallic shells. The inset shows the geometry of the GMG structure. A metallic shell with the dielectric function ε2 = εAg from Johnson and Christy is immersed into and filled with a gain medium with ε3 = ε1 = 2.6+iε1″. The threshold gain values −ε1″ = −εthr″ (left column, log‐color map) and the wavelengths λthr (right) are shown as contour plots as a function of the inner radius a1 and the shell thickness h2. Different plots correspond to different multipolar modes from l = 1 (dipole), to l = 5, as labeled in the panels.
Mentions: The quasi‐static expression (7) shows that for a solid spherical metal particle in a gain medium the dipole mode l=1 is the easiest to generate, as it requires the lowest gain ɛG′′=−ɛM′′/2, while higher multipole thresholds approach the limit ɛG′′=−ɛM′′. For the active void (eq. (8)) the situation is reversed. The dipolar mode requires the largest gainɛG′′=−2ɛM′′, while higher multipoles approach the limit ɛG′′=−ɛM′′. Metallic nano‐shells which have gain both inside and outside (see sketch in the upper right hand corner of Fig. 3), possess both sphere‐ and void‐like features, which makes their ordering of thresholds worth to investigate. For the most of the remaining section, we focus on the symmetric structures, with the same gain material inside and outside a silver shell of radius a1 and thickness h2. A comparison with asymmetric gain distributions, where the gain is either only in the core, or only outside the shell will be given at the end of this section. We will call the symmetric geometry GMG (gain/metal/gain), the case of a gain filled shell with passive dielectric ε3 outside GMε3, and the case of a metallic shell on a gainless core, but with gain outside a ε1MG structure. Asymmetric structures have been discussed before 5, 57, but largely for the quasi‐static dipole case and without global gain optimization via geometry. We note that in the main text, we use full analytical multi‐shell Mie theory without approximations. Quasi‐static approximations can be found in Supp. Info. 6.

Bottom Line: Here, we derive this result from the purely classical electromagnetic scattering framework.Furthermore, retardation is included straightforwardly into our framework; and the global spectral gain minimum persists beyond the quasi-static limit.We illustrate this with two examples of widely used geometries: Silver spheroids and spherical shells embedded in and filled with gain materials.

View Article: PubMed Central - PubMed

Affiliation: Institute of Applied PhysicsJohannes Kepler University LinzAltenbergerstraße 694040 LinzAustria; Soft Matter PhysicsJohannes Kepler University LinzAltenbergerstraße 694040 LinzAustria.

ABSTRACT

It is known (yet often ignored) from quantum mechanical or energetic considerations, that the threshold gain of the quasi-static spaser depends only on the dielectric functions of the metal and the gain material. Here, we derive this result from the purely classical electromagnetic scattering framework. This is of great importance, because electrodynamic modelling is far simpler than quantum mechanical one. The influence of the material dispersion and spaser geometry are clearly separated; the latter influences the threshold gain only indirectly, defining the resonant wavelength. We show that the threshold gain has a minimum as a function of wavelength. A variation of nanoparticle shape, composition, or spasing mode may shift the plasmonic resonance to this optimal wavelength, but it cannot overcome the material-imposed minimal gain. Furthermore, retardation is included straightforwardly into our framework; and the global spectral gain minimum persists beyond the quasi-static limit. We illustrate this with two examples of widely used geometries: Silver spheroids and spherical shells embedded in and filled with gain materials.

No MeSH data available.