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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.


Related in: MedlinePlus

Dipolar thresholds for prolate a) and oblate b) Ag spheroids. Spheroids with ɛ1=ɛAg are immersed in a gain medium with ɛ2=2.6+iɛ2′′. The threshold gain values: −ɛ2′′=−ɛthr′′ are shown at the left ordinate and the generation wavelengths at the right (as indicated by the horizontal arrows), both as functions of the aspect ratio. Insets show the structure geometry with the incident field oriented along the longer axes in both cases. Black solid curves (indexed as c=0 and a=0) correspond to the non‐retarded case. Dashed curves include retardation according to Kuwata. The approximation by Moroz yields similar results as illustrated by the dotted magenta curves. The length of the largest semi‐axis (c for the prolate case in a) and a = b for the oblate case in b) is chosen as the size parameter and is color‐coded in the plots.
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andp201500318-fig-0002: Dipolar thresholds for prolate a) and oblate b) Ag spheroids. Spheroids with ɛ1=ɛAg are immersed in a gain medium with ɛ2=2.6+iɛ2′′. The threshold gain values: −ɛ2′′=−ɛthr′′ are shown at the left ordinate and the generation wavelengths at the right (as indicated by the horizontal arrows), both as functions of the aspect ratio. Insets show the structure geometry with the incident field oriented along the longer axes in both cases. Black solid curves (indexed as c=0 and a=0) correspond to the non‐retarded case. Dashed curves include retardation according to Kuwata. The approximation by Moroz yields similar results as illustrated by the dotted magenta curves. The length of the largest semi‐axis (c for the prolate case in a) and a = b for the oblate case in b) is chosen as the size parameter and is color‐coded in the plots.

Mentions: Spheroidal nanoparticles in gain materials were studied before in the electrostatic limit 45, 56, and experimental results for aggregates of nanoparticles were simulated with spheroids as well 77, 78. In this section, we expand the theoretical considerations to spheroids of finite size where radiation damping and retardation are taken into account. In the non‐retarded case, equations (5) and (6) hold, whereby L=Lz and L=Lx,y for the long axis in the prolate and oblate cases, respectively, are given in Supp. Info. 1. We consider only long wavelength resonances, because the short wavelength resonances overlap with the d‐band absorption and are hence less suited for spasing. The results for the quasistatic, non‐retarded limit are shown in Fig. 2 by black curves.


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

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

Dipolar thresholds for prolate a) and oblate b) Ag spheroids. Spheroids with ɛ1=ɛAg are immersed in a gain medium with ɛ2=2.6+iɛ2′′. The threshold gain values: −ɛ2′′=−ɛthr′′ are shown at the left ordinate and the generation wavelengths at the right (as indicated by the horizontal arrows), both as functions of the aspect ratio. Insets show the structure geometry with the incident field oriented along the longer axes in both cases. Black solid curves (indexed as c=0 and a=0) correspond to the non‐retarded case. Dashed curves include retardation according to Kuwata. The approximation by Moroz yields similar results as illustrated by the dotted magenta curves. The length of the largest semi‐axis (c for the prolate case in a) and a = b for the oblate case in b) is chosen as the size parameter and is color‐coded in the plots.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4834728&req=5

andp201500318-fig-0002: Dipolar thresholds for prolate a) and oblate b) Ag spheroids. Spheroids with ɛ1=ɛAg are immersed in a gain medium with ɛ2=2.6+iɛ2′′. The threshold gain values: −ɛ2′′=−ɛthr′′ are shown at the left ordinate and the generation wavelengths at the right (as indicated by the horizontal arrows), both as functions of the aspect ratio. Insets show the structure geometry with the incident field oriented along the longer axes in both cases. Black solid curves (indexed as c=0 and a=0) correspond to the non‐retarded case. Dashed curves include retardation according to Kuwata. The approximation by Moroz yields similar results as illustrated by the dotted magenta curves. The length of the largest semi‐axis (c for the prolate case in a) and a = b for the oblate case in b) is chosen as the size parameter and is color‐coded in the plots.
Mentions: Spheroidal nanoparticles in gain materials were studied before in the electrostatic limit 45, 56, and experimental results for aggregates of nanoparticles were simulated with spheroids as well 77, 78. In this section, we expand the theoretical considerations to spheroids of finite size where radiation damping and retardation are taken into account. In the non‐retarded case, equations (5) and (6) hold, whereby L=Lz and L=Lx,y for the long axis in the prolate and oblate cases, respectively, are given in Supp. Info. 1. We consider only long wavelength resonances, because the short wavelength resonances overlap with the d‐band absorption and are hence less suited for spasing. The results for the quasistatic, non‐retarded limit are shown in Fig. 2 by black curves.

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.


Related in: MedlinePlus