We report electromagnetically induced gain in a highly degenerate two-level rotational vibrational molecular system. Using two photon (Raman-type) interaction with right and left circularly polarized pump and probe waves, the Zeeman coherence is established within the manifold of degenerate sublevels belonging to a rotational vibrational eigenstate. We analytically and numerically calculate the third-order nonlinear optical susceptibility for a Doppler-broadened molecular transition for an arbitrary high rotational angular momentum $(J\ensuremath{\ge}20)$. It is shown that for a
Q-type open transition, a weak probe will experience an electromagnetically induced gain in presence of a strong copropagating pump wave. The inversionless gain originates due to cancellation of absorption from the interference of the coupled $\ensuremath{\Lambda}$- and V-type excitation channels in an
N-type configuration. A detailed analysis of the optical susceptibility as a function of Doppler detuning explains how the gain bands are generated in a narrow transparency window from the overlapping contributions of different velocity groups. It is shown that the orientation dependent coherent interaction in presence of a strong pump induces narrow resonances for the probe susceptibility. The locations, intensity, and sign (positive or negative susceptibility) of these resonances are decided by the frequency detuning of the Doppler group and the strength of the coupling field. The availability of high power tunable quantum cascade lasers covering a spectral region from about 4 to $12\text{ }\ensuremath{\mu}\text{m}$ opens up the possibility of investigating the molecular vibrational rotational transitions for a variety of coherent effects.
Introduction We were able to show in Chapter 3 that a medium in which we can obtain a population inversion (i.e. a situation in which the population density in the excited state is greater than that in the fundamental level) allows for optical gain of an electromagnetic wave having a frequency near to the resonant frequency of the system. By introducing feedback of the amplified signal into the medium, the system can be made to oscillate naturally, resulting in laser oscillations . To obtain this population inversion, we must introduce at least a third (and perhaps even a fourth) energy level into the system. (We saw how a two-level system under the influence of an intense pump beam will saturate with no resulting population inversion.) The aim then of this chapter is to introduce the concepts necessary to extend our two-level system into a working model capable of illustrating the phenomenon of laser oscillation. We will not spend too much time discussing atomic transition lasers as they do not figure readily in our treatment of quantum electronic properties of semiconductors. An exception will be made, however; we brush upon the particular topics of a diode pumped laser in Complement 4.E and a quantum cascade laser in Complement 13.H. Population inversion and optical amplification Population inversion We will show how population inversion can be achieved by carrier transfer from higher lying levels to the upper level of a two-level subsystem of interest.
The emergence of laser action from an atomic system without population inversion is beginning to attract theoretical and experimental attention as a possible way of generating useful coherent radiation at unusual wavelengths. The goal of this communication is to clarify the physical origin of this phenomenon using a four-level system whose ground state consists of two quasidegenerate levels that are coupled to a higher-lying state by a Raman-like transition. In the presence of the ground-state coherence induced by the Raman field, we calculate the absorption spectrum of a weak probe whose tunable frequency scans across the transition frequencies between the two ground-state levels and another higher-lying state that may or may not be weakly excited by an incoherent pump mechanism. Our calculation, based on a dressed atomic state approach, clarifies the conditions that must be satisfied to produce gain, identifies the frequency (or frequencies) at which the gain is maximum, and elucidates the functions of the incoherent pump, the Raman field, and the coherence between the ground-state levels in this process. An appropriate set of Maxwell- Bloch equations for a ring-cavity model of this system confirms the appearance of laser action when the small-signal gain conditions are satisfied.
We pump low-pressure nitrogen gas with ionizing femtosecond laser pulses at 1.5 $\ensuremath{\mu}\mathrm{m}$ wavelength. The resulting rotationally excited
N2+ molecular ions generate directional, forward-propagating stimulated and isotropic spontaneous emissions at 428 nm wavelength. Through high-resolution spectroscopy of these emissions, we quantify rotational population distributions in the upper and lower emission levels. We show that these distributions are shifted with respect to each other, which has a strong influence on the transient optical gain in this system. Although we find that electronic population inversion exists in our particular experiment, we show that sufficient dissimilarity of rotational distributions in the upper and lower emission levels could, in principle, lead to gain without net electronic population inversion.
This paper presents observations and an interpretation of laser-induced excitation and fluorescence in a ladder $g\text{\ensuremath{-}}e\text{\ensuremath{-}}f$ of three molecular levels [$X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}({v}^{\ensuremath{''}}=0,{J}^{\ensuremath{''}}=7)$, $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}({v}^{\ensuremath{'}}=10,{J}^{\ensuremath{'}}=8)$, and $5\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}(v=10,J=9)$, respectively] observed in a supersonic molecular beam of
Na2. The $g\text{\ensuremath{-}}e$ coupling, by cw laser
P, is strong. A weak cw laser
S couples levels
e and
f. The basic observations are of level-
f fluorescence as a function of the detuning of the
S laser from resonance. The signal profile does not appear as the typical Autler-Townes doublet, but as a spectral structure, whose position, width, and shape depend upon several laser parameters. We interpret these results using a simple model of three nondegenerate quantum states coherently excited while undergoing population loss to states outside the three-level system. We invoke the mechanism of optical pumping and evolution along adiabatic states, together with Landau-Zener transition probabilities. We also present results from numerical studies, which include all quantum states, all radiative couplings, coherent and incoherent, as well as convolutions with the relevant distribution functions (velocities and Zeeman sublevels). Although no adjustable parameters are involved, excellent agreement with the experiment is found. Since successive avoided crossings of adiabatic eigenvalues occur, interference effects may be relevant. Such effects are not expected to be visible in the present experiment, for reasons that are discussed. However, we discuss conditions which would allow resolving the interference structure experimentally. We also suggest possible interesting applications of the interference to rapidly switch off Rydberg state population or to control its spatial distribution.
A three-level system which radiates at both intermediate transition frequencies is considered to be coherently pumped at a frequency near the two-photon resonance frequency. A sharply resonant rise in the second- and third-level population is found for slight detuning of the pump from two-photon resonance. Population inversion in either transition is shown to be possible, depending on the pertinent parameters. This effect furnishes a novel method of population inversion at a frequency higher than the pump frequency. Keywords include: Laser, Laser-type devices, Coherent pumping, Three-level systems, and Quantum electronics.