@article { ISI:000225223700006,
	title = {Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers},
	journal = {IEEE JOURNAL OF QUANTUM ELECTRONICS},
	volume = {40},
	number = {12},
	year = {2004},
	month = {DEC},
	pages = {1663-1674},
	publisher = {IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC},
	type = {Article},
	address = {445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA},
	abstract = {A theoretical and experimental study of the optical gain and the linewidth enhancement factor (LEF) of a type-I quantum-cascade (QQ laser is reported. QC lasers have a symmetrical gain spectrum because the optical transition occurs between conduction subbands. According to the Kramers-Kronig relation, a zero LEF is predicted at the gain peak, but there has been no experimental observation of a zero LEF. There are other mechanisms that affect the LEF such as device self-heating, and the refractive index change due to other transition states not involved in lasing action. In this paper, the effects of these mechanisms on the LEF of a type-I QC laser are investigated theoretically and experimentally. The optical gain spectrum and the LEF are measured using the Hakki-Paoli method. Device self-heating on the wavelength shift in the Fabry-Perot modes is isolated by measuring the shift of the lasing wavelength above the threshold current. The band structure of a QC laser is calculated by solving the Schrodinger-Poisson equation self-consistently. We use the Gaussian lineshape function for gain change and the confluent hypergeometric function of the first kind for refractive index change, which satisfies the Kramers-Kronig relation. The refractive index change caused by various transition states is calculated by the theoretical model of a type-I QC laser. The calculated LEF shows good agreement with the experimental measurement.},
	keywords = {intersubband transition, linewidth enhancement factor (LEF), quantum-cascade (QC)laser},
	issn = {0018-9197},
	doi = {10.1109/JQE.2004.837666},
	author = {Kim, J. and Lerttamrab, M and Chuang, SL and Gmachl, C. and Sivco, DL and F. Capasso and Cho, AY}
}
