The gain and carrier density in semiconductor lasers under steady-state and transient conditions

Abstract

Abstract-The carrier distribution functions in a semiconductor crystal in the presence of a strong optical field are obtained. These are used to derive expressions for the gain dependence on the carrier density and on the optical intensitythe gain suppression effect. A general expression for high order nonlinear gain coefficients is obtained. This formalism is then used to describe the carrier and power dynamics in semiconductor lasers above and below threshold in the static and transient regimes.

High-power blue superluminescent diode for high CRI lighting and high-speed visible light communication

“…4(a). By increasing the current density (J), it is expected that the active region carrier concentration (N) increases, leading to a decrease in the differential carrier lifetime (τ) [49,50]. This differential lifetime is inversely proportional to the frequency modulation bandwidth (f 3dB ), given by 3 ( 3 / 2 ) dB f πτ = , leading to incremental modulation bandwidths at higher injection currents [51,52].…”

High‐Q, Low‐Threshold Monolithic Perovskite Thin‐Film Vertical‐Cavity Lasers

“…While for the falling edge, the lasing pulses synchronize with the excitation pulse as carriers supplied from the excitation pulse are insufficient to maintain laser oscillation condition. For microscopic insight, we applied a classical rate equation analysis to model the coupled carrier and photon density dynamics upon excitation. By constructing an analytical gain model and iteratively fitting the result of L–L curve data (both threshold energy density and phase transition “kink” from spontaneous emission to lasing) and the corresponding PeVCSEL temporal pulse shapes under different pump fluences (see the Supporting Information and Figure S6–S8, Supporting Information, for detail), we obtain carrier density dependent gain coefficient of perovskite film which converges to a gain coefficient at threshold of g th ≈ 378 cm −1 .…”

“…For microscopic insight, we applied a classical rate equation analysis to model the coupled carrier and photon density dynamics upon excitation. By constructing an analytical gain model and iteratively fitting the result of L–L curve data (both threshold energy density and phase transition “kink” from spontaneous emission to lasing) and the corresponding PeVCSEL temporal pulse shapes under different pump fluences (see the Supporting Information and Figure S6–S8, Supporting Information, for detail), we obtain carrier density dependent gain coefficient of perovskite film which converges to a gain coefficient at threshold of g th ≈ 378 cm −1 . Based on the value of threshold gain (also indicates the total loss needs to be overcome to achieve lasing condition), we calculate the cavity quality factor Q ≈ 1.1 × 10 3 , corresponding to a cold cavity mode linewidth (Δλ = λ/ Q ) Δλ ≈ 0.71 nm.…”

Stable Green Perovskite Vertical-Cavity Surface-Emitting Lasers on Rigid and Flexible Substrates

“…Rather, in the lasing regime the linewidth is fundamentally limited by and originates from the phase and amplitude noise as spontaneous emission is coupled into the lasing mode . For microscopic insight, we apply a classic rate-equation analysis − to model the coupled carrier and photon density dynamics upon excitation (Supporting Information, eqs S4–S6, Figures S5–S7). By fitting the L–L curve data (both threshold energy density and phase transition “kink” from spontaneous emission to lasing, green line in Figure a), we estimate the spontaneous emission factor β ∼ 0.02, which is consistent with values from other similar optically pumped inorganic semiconductor VCSEL structures, such as III–V nitrides …”