Self-consistent calculation of metamaterials with gain

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 24, 2009, Pages

  Fang, A ^a   Koschny, Th ^a,b   Wegener, M ^c   Soukoulis, C M ^a,b  

^a IOWA STATE UNIVERSITY   (United States)

^b INSTITUTE OF ELECTRONIC STRUCTURE AND LASER   (Greece)

^c UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650073269     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.241104     Document Type: Article

References (23)

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10. The real and the imaginary parts of the gain profile are given by P/ ε0 E= χ′ +i χ″, where χ′ =- χ0″ Δx/ (1+Δ x2) and χ″ = χ0″ / (1+Δ x2) with Δx=2 (ω- ωa) / Γa and χ0″ =- σa ΔN/ (ε0 ωa Γa), where ΔN= N2 - N1.
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14. We first check that a well-defined lasing threshold exists for a gain material slab with a width of 500 nm. The pumping rate for lasing threshold is 1.6× 109 s-1, which corresponds to the incident power of 65W/ mm2 and the output power is 4× 10-3 W/ mm2. If the pumping rate is much higher than the lasing threshold, i.e., 3.5× 109 s-1, the occupation numbers N2 and N1 oscillate as a function of time and finally saturate to the stable values. For the parameters used, N2 7.5× 10-3 N0 and N1 2.0× 10-4 N0.
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21. The extinction coefficient (amplification coefficient) of the gain material can be calculated from α=ω χ″ / (2c εr) given in Chap. 7 of Ref.. For the pumping rate Γpump =1.4× 109 s-1 and f=100THz, we obtain ΔN=6.9× 10-3 Ni [Ni = No (t=0) =5.0× 1023 / m3], and hence α=-1.50× 103 cm-1 at the resonance. In our case for 97 THz, we get α=-1.39× 103 cm-1.
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