FDTD SIMULATION OF COOPERATIVE EMISSION IN SEMICONDUCTOR LASER UNDER DC PUMPING CURRENT
Y. O. Katsiashou*, V. V. Makarevich
Mogilev State University, Kosmonavtov 1, Mogilev, Belarus
*Mogilev State University, Kosmonavtov 1, Mogilev, Belarus, eugene.kotyashov@gmail.com
The possibility of generation of ultrashort pulses via cooperative laser action in Fabri-Perrot cavity under continuous pumping was investigated numerically. Coherent interaction of radiation with active particles of gain medium is described by a system of Maxwell-Bloch equations:
P abE 2 d ω0 4 Ω 0) N nr (N γ 2Λ N abEN, 1 d Ω
2 ω0 2P ω0 P 2γ P abP, ad 2n 0E εε D , t H µµ 0 rotE , t
rotH D &
h
&
h
&
&
& + + = = − − − −
+
∂ =
− ∂
∂ =
= ∂
where γ – the relaxation frequency of polarization, γnr – the relaxation frequency of inversion, na – the density of active particles, ω0 – the two-level transition frequency, N0 – the inversion at the thermal equilibrium state, N – the inversion rate(-1 at totally excited state and 1 at the ground state), P – the polarization degree of active particles, E – the electric field, D – the electric displacement field, H – the magnetic field, ε0 – the vacuum permittivity, ε – the medium permittivity, µ0 – the vacuum permeability, µ – the medium permeability, Ω = (ω0
2 – γ2)1/2 , Λ - the pumping rate.
Parameters used for calculations were typical for semiconductor materials, like GaAs: ω0 = 3·1015 Hz, γnr = 3·108 Hz, γ = 1·1013 Hz, dab = - 1.9·10-29 A·s·m, N0 = 1, na = 5·1026 m-3, λ = 2πc/ω0 ≈ 630 nm.
a) b) c)
d) e) f)
g) h) i)
(a) Laser model, used in numerical calculations, L – total resonator length, l – active resonator part lengt. (b) Dependence of output electric field on time at L = 2.5λ and Λ = 6•1010 s-1, and spectrum (c). (d) Individual pulse intensity shape fitting with I(t) = sech2(t/tp). e) Dependence of pulse spacing (e) and duration (f) on pumping rate at L = 0.5λ, (g) diagram of pulsed modes, pumping rate – active medium length diagram. All figures (b) – (f) are have resonator fill factor l/L set to 1. The intensity time dependency (h) and appropriate spectrum (i) for small fill factor l/L < 0.01 shows periodicity with resonator round trip time.
The calculation results illustrates possibility of various pulsed modes in coherent regime. When fill factor l/L is one there is a strong dependence of pulse length and repetition rate on the pump rate. The pulse duration is in the order of 150 fs. The small fill factor enable of quasimodelocked regime with some hundreds of femtoseconds pulse length and pump power independent repetition rate.
PML PML
L l
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