Theory of Cooperative Cascade Emission. I. Linear Stochastic Theory

Observation of picosecond superfluorescent pulses in rubidium atomic vapor pumped by 100-fs laser pulses

“…Assuming that the backward 5 µm SF is uncoupled from the forward 5 µm and forward 420 nm SF, the Maxwell equations for two copropagating modes in the retarded time frame t → t − z/c, are given by [15,17,22] …”

“…In this case, the initial populations of the upper and lower states are the control parameters rather than input pump power. This model of copropagating modes for cascade three-level atoms has been studied in [15,22] where the backward propagating mode is assumed to be generated independently. The reduced equation of motion for three-level atoms can be obtained from the five-level case by eliminating levels |b 1 and |b 2 .…”

“…For the sake of simplicity, assume that the populations of the levels are time independent and expressed by their initial values [i.e., ρ cc (t) ρ cc (0), ρ aa (t) ρ aa (0), and ρ bb (t) 0]. In the linear approximation [22], nonlinear terms bc ρ ab and ab ρ bc are neglected; thus, ρ ac (t) ρ ac (0). Similarly, as found in [15,17,22], the Rabi frequencies are given by 4), we infer the characteristic exponential growth [22] of the emissions on both the upper (ab) and lower (bc) transitions (i.e., both the 5 µm and 420 nm pulses are SF emissions [17]).…”

“…In the linear approximation [22], nonlinear terms bc ρ ab and ab ρ bc are neglected; thus, ρ ac (t) ρ ac (0). Similarly, as found in [15,17,22], the Rabi frequencies are given by 4), we infer the characteristic exponential growth [22] of the emissions on both the upper (ab) and lower (bc) transitions (i.e., both the 5 µm and 420 nm pulses are SF emissions [17]). The growth rate does depend solely on the main parameter ξ leading to yoked SF [17].…”

“…Inclusion of all SF pulses simultaneously in the general Maxwell equations is cumbersome. In the previous section it is assumed that the SF emissions in the forward and backward directions are independent [17,22] (i.e., the backward 5 µm SF is uncoupled from the forward 5 µm SF and forward 420 nm SF). In contrast, let us assume here that the backward 5 µm SF and forward 420 nm SF are coupled, and the forward 5 µm SF is independent.…”