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Physical Review A

Theoretical scheme for lasing without population inversion in the H2 molecule

Lipika Adhya, S. Sanyal, Krishna Rai Dastidar

Published Nov 1, 1995• 6 citations
Publisher

Abstract

We have shown that (1+1\ensuremath{'})-photon lasing without population inversion (LWOPI) can be achieved in a ${\mathrm{H}}_{2}$ molecule for emission from the lowest doubly excited autoionizing (AI) state of $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}$ symmetry to the ground X${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}$ (v=0,j=1) state in the presence of the resonant B${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}$ (v=4,j=2) level. We have considered both coherent and incoherent pumping of the AI state, which is the upper lasing level in this scheme. Coherent pumping of the AI state can be done by two-photon excitation from the ground to the AI state. Incoherent pumping of the AI state can be done by charge-transfer collision of a ${\mathrm{H}}_{2}^{+}$ ion with atomic and molecular species. For a weak coherent pumping field of intensity 6.4\ifmmode\times\else\texttimes\fi{}${10}^{7}$ W/${\mathrm{cm}}^{2}$, a lower probe field [for the X${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}$ (v=0,j=1)\ensuremath{\rightleftarrows}B${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}$ (v=4,j=2) transition] of intensity 9.6\ifmmode\times\else\texttimes\fi{}${10}^{6}$ W/${\mathrm{cm}}^{2}$ is required to obtain an appreciable gain. However, for stronger coherent fields of intensity 6.4\ifmmode\times\else\texttimes\fi{}${10}^{9}$ W/${\mathrm{cm}}^{2}$, the lower probe intensity can be lowered by orders of magnitude without significant loss in gain. In this case, using a lower probe field of intensity 9.6\ifmmode\times\else\texttimes\fi{}${10}^{4}$ W/${\mathrm{cm}}^{2}$, we have calculated the gain by the perturbative method. However, for a lower value of coherent field strength, 6.4\ifmmode\times\else\texttimes\fi{}${10}^{7}$ W/${\mathrm{cm}}^{2}$, and a higher intensity of the lower probe field, 9.6\ifmmode\times\else\texttimes\fi{}${10}^{6}$ W/${\mathrm{cm}}^{2}$, we have done nonperturbative calculations and have shown that LWOPI can be achieved only in a short range of probe pulse duration less than or equal to 3.45 ps. In all these cases, the optimum intensity for the upper probe field [for the B${\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}$ (v=4,j=2)${\ensuremath{\rightleftarrows}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}}$ transition] is 9.6\ifmmode\times\else\texttimes\fi{}${10}^{7}$ W/${\mathrm{cm}}^{2}$. We have also compared the evolution of gain for the ${\mathrm{sech}}^{2}$(t/T)-shaped pulse with that for the square pulse, the pulse duration T=3.45 ps being the same in both cases.

DOI
10.1103/physreva.52.4078

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We have shown that (1+1\ensuremath{'})-photon lasing without population inversion (LWOPI) can be achieved in a H2{\mathrm{H}}_{2}H2​ molecule for emission from the lowest doubly excited autoionizing (AI) state of 1\ensuremathΣg^{1}\mathrm{\ensuremath{\Sigma}}_{\mathit{g}}1\ensuremathΣg​ symmetry to the ground X{\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}} (v=0,j=1) state in the presence of the resonant B{\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}} (v=4,j=2) level. We have considered both coherent and incoherent pumping of the AI state, which is the upper lasing level in this scheme. Coherent pumping of the AI state can be done by two-photon excitation from the ground to the AI state. Incoherent pumping of the AI state can be done by charge-transfer collision of a H2+{\mathrm{H}}_{2}^{+}H2+​ ion with atomic and molecular species. For a weak coherent pumping field of intensity 6.4\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2, a lower probe field [for the X{\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}} (v=0,j=1)\ensuremath{\rightleftarrows}B{\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}} (v=4,j=2) transition] of intensity 9.6\ifmmode\times\else\texttimes\fi{}106{10}^{6}106 W/cm2{\mathrm{cm}}^{2}cm2 is required to obtain an appreciable gain. However, for stronger coherent fields of intensity 6.4\ifmmode\times\else\texttimes\fi{}109{10}^{9}109 W/cm2{\mathrm{cm}}^{2}cm2, the lower probe intensity can be lowered by orders of magnitude without significant loss in gain. In this case, using a lower probe field of intensity 9.6\ifmmode\times\else\texttimes\fi{}104{10}^{4}104 W/cm2{\mathrm{cm}}^{2}cm2, we have calculated the gain by the perturbative method. However, for a lower value of coherent field strength, 6.4\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2, and a higher intensity of the lower probe field, 9.6\ifmmode\times\else\texttimes\fi{}106{10}^{6}106 W/cm2{\mathrm{cm}}^{2}cm2, we have done nonperturbative calculations and have shown that LWOPI can be achieved only in a short range of probe pulse duration less than or equal to 3.45 ps. In all these cases, the optimum intensity for the upper probe field [for the B{\mathrm{}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}} (v=4,j=2){\ensuremath{\rightleftarrows}}^{1}$${\mathrm{\ensuremath{\Sigma}}}_{\mathit{g}} transition] is 9.6\ifmmode\times\else\texttimes\fi{}107{10}^{7}107 W/cm2{\mathrm{cm}}^{2}cm2. We have also compared the evolution of gain for the sech2{\mathrm{sech}}^{2}sech2(t/T)-shaped pulse with that for the square pulse, the pulse duration T=3.45 ps being the same in both cases.
Summary form only given. We study a model for an incoherently pumped laser operating with a Doppler-broadened three-level system placed in a doubly resonant cavity and producing two laser fields, one of them without population inversion. Each laser field couples to only one of the transitions of the three-level medium. We have studied our model for parameters appropriate to two real atomic systems (i) a cascade scheme in atomic /sup 138/Ba looking for lasing with (without) inversion at /spl lambda//sub /spl beta//=554 nm (/spl lambda//sub /spl alpha//=821 nm), and (ii) a V-scheme in atomic /sup 85/Rb with ordinary lasing at /spl lambda//sub /spl alpha//=780 nm and lasing without inversion (LWI) at /spl lambda//sub /spl alpha//=4216 nm. These two cases are qualitatively different in that two-photon processes are responsible for inversionless gain in case (i) while LWI in case (ii) arises from one-photon processes. Moreover, the frequency up-conversion ratio is R=0.67 for the case of /sup 138/Ba and it is R=1.88 for the case of /sup 85/Rb. In spite of the fact that the frequencies of the two laser fields are relatively different, our results show that dual-wavelength lasing extends up to Doppler broadening values typical for optical transitions of atoms in a vapor cell. In case (i) /spl alpha/-lasing occurs without two-photon inversion only for approximately the lower half of the domain of Doppler-broadening values. However, in case (ii) one has LWI in all the domains. Some considerations for a practical realization of the dual-wavelength inversionless-conventional laser are discussed.
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.
In a time-dependent dressed-state calculation we have studied the time development of (1+1)-photon amplification without population inversion from an autoionizing (AI) state which is coupled to another AI state embedded into the same continuum. We have shown that the (1+1)-photon gain evolves with time over the single-photon gain and it can be controlled by changing the relative strength of the coupling of the resonant intermediate state with the ground state and with the two AI states. We have also shown that three-peaked gain on the upper probe field evolves with time and we have demonstrated that the modification of the second peak and the appearance of the third peak are solely due to the presence of the second AI state.
We experimentally demonstrate the existence of long-lived coherent polarizations coupling simultaneously ground state X (X2Σg+) to excited states A (A2Πu) and B (B2Σu+) of N2+ inside a plasma created by a short intense laser pulse at 800 nm. This three-level V-scheme arrangement is responsible for a strong optical gain without population inversion at the B–X transition at 391.4 nm. Simulations based on Maxwell-Bloch equations reproduce well the kinetics and the pressure dependence of the gain.
We have come to think that lasing requires an inversion of population between atoms in an excited state and those in a lower state: Normally the probability of absorption from the lower state equals the probability of emission from the higher state, so that the only way to have more photons coming out than going in is to start with more atoms in the upper state. It would be useful to decouple the probabilities of emission and absorption, so that one could lower the loss associated with absorption without reducing the emission.