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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.


Comparison of the field enhancement /E//E0 between the GMG (a) and GMG1 (b) structures near the generation threshold of the l = 3 mode. In both cases, Johnson and Christy data are used for Ag, and εG = 2.6‐0.08i. a1 = 50 nm and h2 = 5 nm for both structures, and h3 = 50 nm in case of the GMG1 structure. The propagation direction and the polarization of the incident plane wave with the amplitude E0 are indicated in panel a).
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andp201500318-fig-0004: Comparison of the field enhancement /E//E0 between the GMG (a) and GMG1 (b) structures near the generation threshold of the l = 3 mode. In both cases, Johnson and Christy data are used for Ag, and εG = 2.6‐0.08i. a1 = 50 nm and h2 = 5 nm for both structures, and h3 = 50 nm in case of the GMG1 structure. The propagation direction and the polarization of the incident plane wave with the amplitude E0 are indicated in panel a).

Mentions: An infinite gain medium may contain exponentially growing solutions. This is known to cause non‐trivial issues in Fresnel formulas, as well as in total internal reflection (see 82 and refs. therein). However, these issues do not influence the threshold gain and wavelength, obtained from zeroes of scattering denominators, which are related to the multipolar solutions of plasmonic structures, even if the corresponding outgoing scattered waves are amplified at larger distances. To illustrate this, we compare the GMG structure studied in Fig. 3 with a GMG1 structure, where a gain containing core (a1=50 nm ) is covered by a silver shell (h2=5 nm ) and by a gain‐shell (h3=50 nm ), followed by vacuum. We find that the difference is not substantial, because the relevant field structures are very similar near the metallic shell. This is illustrated in Fig. 4 for the l = 3 mode. For such a GMG structure, the enhanced field near the metallic shell initially decays on a length scale comparable to the radius of the inner core (50 nm). Figure 4b shows that for the GMG1 structure most of the enhanced field remains inside the 50 nm thick outer gain shell.


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

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

Comparison of the field enhancement /E//E0 between the GMG (a) and GMG1 (b) structures near the generation threshold of the l = 3 mode. In both cases, Johnson and Christy data are used for Ag, and εG = 2.6‐0.08i. a1 = 50 nm and h2 = 5 nm for both structures, and h3 = 50 nm in case of the GMG1 structure. The propagation direction and the polarization of the incident plane wave with the amplitude E0 are indicated in panel a).
© Copyright Policy - creativeCommonsBy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4834728&req=5

andp201500318-fig-0004: Comparison of the field enhancement /E//E0 between the GMG (a) and GMG1 (b) structures near the generation threshold of the l = 3 mode. In both cases, Johnson and Christy data are used for Ag, and εG = 2.6‐0.08i. a1 = 50 nm and h2 = 5 nm for both structures, and h3 = 50 nm in case of the GMG1 structure. The propagation direction and the polarization of the incident plane wave with the amplitude E0 are indicated in panel a).
Mentions: An infinite gain medium may contain exponentially growing solutions. This is known to cause non‐trivial issues in Fresnel formulas, as well as in total internal reflection (see 82 and refs. therein). However, these issues do not influence the threshold gain and wavelength, obtained from zeroes of scattering denominators, which are related to the multipolar solutions of plasmonic structures, even if the corresponding outgoing scattered waves are amplified at larger distances. To illustrate this, we compare the GMG structure studied in Fig. 3 with a GMG1 structure, where a gain containing core (a1=50 nm ) is covered by a silver shell (h2=5 nm ) and by a gain‐shell (h3=50 nm ), followed by vacuum. We find that the difference is not substantial, because the relevant field structures are very similar near the metallic shell. This is illustrated in Fig. 4 for the l = 3 mode. For such a GMG structure, the enhanced field near the metallic shell initially decays on a length scale comparable to the radius of the inner core (50 nm). Figure 4b shows that for the GMG1 structure most of the enhanced field remains inside the 50 nm thick outer gain shell.

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.